# 2.1 Solve equations using the subtraction and addition properties  (Page 5/6)

 Page 5 / 6

## Practice makes perfect

Verify a Solution of an Equation

In the following exercises, determine whether the given value is a solution to the equation.

Is $y=\frac{5}{3}$ a solution of
$6y+10=12y$ ?

yes

Is $x=\frac{9}{4}$ a solution of
$4x+9=8x$ ?

Is $u=-\frac{1}{2}$ a solution of
$8u-1=6u$ ?

no

Is $v=-\frac{1}{3}$ a solution of
$9v-2=3v$ ?

Solve Equations using the Subtraction and Addition Properties of Equality

In the following exercises, solve each equation using the Subtraction and Addition Properties of Equality.

$x+24=35$

$x=11$

$x+17=22$

$y+45=-66$

$y=-111$

$y+39=-83$

$b+\frac{1}{4}=\frac{3}{4}$

$b=\frac{1}{2}$

$a+\frac{2}{5}=\frac{4}{5}$

$p+2.4=-9.3$

$p=-11.7$

$m+7.9=11.6$

$a-45=76$

$a=121$

$a-30=57$

$m-18=-200$

$m=-182$

$m-12=-12$

$x-\frac{1}{3}=2$

$x=\frac{7}{3}$

$x-\frac{1}{5}=4$

$y-3.8=10$

$y=13.8$

$y-7.2=5$

$x-165=-420$

$x=-255$

$z-101=-314$

$z+0.52=-8.5$

$z=-9.02$

$x+0.93=-4.1$

$q+\frac{3}{4}=\frac{1}{2}$

$q=-\frac{1}{4}$

$p+\frac{1}{3}=\frac{5}{6}$

$p-\frac{2}{5}=\frac{2}{3}$

$p=\frac{16}{15}$

$y-\frac{3}{4}=\frac{3}{5}$

Solve Equations that Require Simplification

In the following exercises, solve each equation.

$c+31-10=46$

$c=25$

$m+16-28=5$

$9x+5-8x+14=20$

$x=1$

$6x+8-5x+16=32$

$-6x-11+7x-5=-16$

$x=0$

$-8n-17+9n-4=-41$

$5\left(y-6\right)-4y=-6$

$y=8$ $y=24$

$9\left(y-2\right)-8y=-16$

$8\left(u+1.5\right)-7u=4.9$

$u=-7.1$

$5\left(w+2.2\right)-4w=9.3$

$6a-5\left(a-2\right)+9=-11$

$a=-30$

$8c-7\left(c-3\right)+4=-16$

$6\left(y-2\right)-5y=4\left(y+3\right)$
$-4\left(y-1\right)$

$y=28$

$9\left(x-1\right)-8x=-3\left(x+5\right)$
$+3\left(x-5\right)$

$3\left(5n-1\right)-14n+9$
$=10\left(n-4\right)-6n-4\left(n+1\right)$

$n=-50$

$2\left(8m+3\right)-15m-4$
$=9\left(m+6\right)-2\left(m-1\right)-7m$

$\text{−}\left(j+2\right)+2j-1=5$

$j=8$

$\text{−}\left(k+7\right)+2k+8=7$

$\text{−}\left(\frac{1}{4}a-\frac{3}{4}\right)+\frac{5}{4}a=-2$

$a=-\frac{11}{4}$

$\text{−}\left(\frac{2}{3}d-\frac{1}{3}\right)+\frac{5}{3}d=-4$

$8\left(4x+5\right)-5\left(6x\right)-x$
$=53-6\left(x+1\right)+3\left(2x+2\right)$

$x=13$

$6\left(9y-1\right)-10\left(5y\right)-3y$
$=22-4\left(2y-12\right)+8\left(y-6\right)$

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve it.

Nine more than $x$ is equal to 52.

$x+9=52;x=43$

The sum of x and $-15$ is 23.

Ten less than m is $-14$ .

$m-10=-14;m=-4$

Three less than y is $-19$ .

The sum of y and $-30$ is 40.

$y+\left(-30\right)=40;y=70$

Twelve more than p is equal to 67.

The difference of $9x\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8x$ is 107.

$9x-8x=107;107$

The difference of $5c\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}4c$ is 602.

The difference of $n$ and $\frac{1}{6}$ is $\frac{1}{2}$ .

$n-\frac{1}{6}=\frac{1}{2};\frac{2}{3}$

The difference of $f$ and $\frac{1}{3}$ is $\frac{1}{12}$ .

The sum of $-4n$ and $5n$ is $-82$ .

$-4n+5n=-82;-82$

The sum of $-9m$ and $10m$ is $-95$ .

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Distance Avril rode her bike a total of 18 miles, from home to the library and then to the beach. The distance from Avril’s house to the library is 7 miles. What is the distance from the library to the beach?

11 miles

Reading Jeff read a total of 54 pages in his History and Sociology textbooks. He read 41 pages in his History textbook. How many pages did he read in his Sociology textbook?

Age Eva’s daughter is 15 years younger than her son. Eva’s son is 22 years old. How old is her daughter?

7 years old

Age Pablo’s father is 3 years older than his mother. Pablo’s mother is 42 years old. How old is his father?

Groceries For a family birthday dinner, Celeste bought a turkey that weighed 5 pounds less than the one she bought for Thanksgiving. The birthday turkey weighed 16 pounds. How much did the Thanksgiving turkey weigh?

21 pounds

Weight Allie weighs 8 pounds less than her twin sister Lorrie. Allie weighs 124 pounds. How much does Lorrie weigh?

Health Connor’s temperature was 0.7 degrees higher this morning than it had been last night. His temperature this morning was 101.2 degrees. What was his temperature last night?

100.5 degrees

Health The nurse reported that Tricia’s daughter had gained 4.2 pounds since her last checkup and now weighs 31.6 pounds. How much did Tricia’s daughter weigh at her last checkup?

Salary Ron’s paycheck this week was $17.43 less than his paycheck last week. His paycheck this week was$103.76. How much was Ron’s paycheck last week?

$121.19 Textbooks Melissa’s math book cost$22.85 less than her art book cost. Her math book cost $93.75. How much did her art book cost? ## Everyday math Construction Miguel wants to drill a hole for a $\frac{5}{8}$ inch screw. The hole should be $\frac{1}{12}$ inch smaller than the screw. Let $d$ equal the size of the hole he should drill. Solve the equation $d-\frac{1}{12}=\frac{5}{8}$ to see what size the hole should be. $d=\frac{17}{24}\phantom{\rule{0.2em}{0ex}}\text{inch}$ Baking Kelsey needs $\frac{2}{3}$ cup of sugar for the cookie recipe she wants to make. She only has $\frac{3}{8}$ cup of sugar and will borrow the rest from her neighbor. Let $s$ equal the amount of sugar she will borrow. Solve the equation $\frac{3}{8}+s=\frac{2}{3}$ to find the amount of sugar she should ask to borrow. ## Writing exercises Is $-8$ a solution to the equation $3x=16-5x$ ? How do you know? No. Justifications will vary. What is the first step in your solution to the equation $10x+2=4x+26$ ? ## Self check After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. If most of your checks were: …confidently. Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific! …with some help. This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential - every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved? …no - I don’t get it! This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need. #### Questions & Answers How do you find divisible numbers without a calculator? Jacob Reply TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13 BAINAMA When she graduates college, Linda will owe$43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan? Ariana Reply Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus? Kirisma Reply 66miles/hour snigdha How did you work it out? Esther s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr Orlando hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused. Alicia Reply what do you need help in? Felix subtracting a negative....is adding!! Heather look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number... Felix for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer... Felix —12 Niazmohammad Thanks Felix.l also get confused with signs. Esther Thank you for this Shatey ty Graham think about it like you lost$19 (-19), then found $7(+7). Totally you lost just$12 (-12)
Annushka
I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
John Reply
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
achol Reply
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce
where's the answers?
Ed Reply
I don't see where the answers are.
Ed
Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?
Maddy Reply
3
Christopher
18t+14t=96 32t=96 32/96 3
Christopher
show that a^n-b^2n is divisible by a-b
Florence Reply
What does 3 times your weight right now
Cherokee Reply
Use algebra to combine 39×5 and the half sum of travel of 59+30
Cherokee
What is the segment of 13? Explain
Cherokee
my weight is 49. So 3 times is 147
Cherokee
kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps
tyler
How to convert grams to pounds?
paul
What is the lcm of 340
Kendra Reply
Yes
Cherokee
How many numbers each equal to y must be taken to make 15xy
Malik Reply
15x
Martin
15x
Asamoah
15x
Hugo
1y
Tom
1y x 15y
Tom
find the equation whose roots are 1 and 2
Adda Reply
(x - 2)(x -1)=0 so equation is x^2-x+2=0
Ranu
I believe it's x^2-3x+2
NerdNamedGerg
because the X's multiply by the -2 and the -1 and than combine like terms
NerdNamedGerg
find the equation whose roots are -1 and 4
Adda
Ans = ×^2-3×+2
Gee
find the equation whose roots are -2 and -1
Adda
(×+1)(×-4) = x^2-3×-4
Gee
yeah
Asamoah
Quadratic equations involving factorization
Winner Reply
there's a chatting option in the app wow
Nana
That's cool cool
Nana
Nice to meet you all
Nana
you too.
Joan
😃
Nana
Hey you all there are several Free Apps that can really help you to better solve type Equations.
Debra
Debra, which apps specifically. ..?
Nana
am having a course in elementary algebra ,any recommendations ?
samuel
Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science
Nana
me too as part of my core subjects in R M E
Ken
at ABETIFI COLLEGE OF EDUCATION
Ken
ok great. Good to know.
Joan
5x + 1/3= 2x + 1/2
sanam
Plz solve this
sanam
5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12
Ranu
Thks ranu
sanam
Please help me solve this 10x+14=-2x+38
Erica
the previous equation should be 3x = 1/6 x=1/18
Sriram
for the new one 10x + 2x = 38 - 14
Sriram
12x = 24 x=2
Sriram
10x + 14 = -2x +38 10x + 2x = 38 - 14 12x = 24 divide both sides by the coefficient of x, which is 12 therefore × = 2
vida
a trader gains 20 rupees loses 42 rupees and then gains ten rupees Express algebraically the result of his transactions
vinaya Reply
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya
a trader gains 20 rupees loses 42 rupees and then gains 10 rupees Express algebraically the result of his three transactions
vinaya

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