2.2 Solve equations using the division and multiplication properties  (Page 4/4)

 Page 4 / 4

$120,000 Translate and solve: Stella planted 14 flats of flowers in $\frac{2}{3}$ of her garden. How many flats of flowers would she need to fill the whole garden? 21 flats Key concepts • The Division Property of Equality —For any numbers a , b , and c , and $c\ne 0$ , if $a=b$ , then $\frac{a}{c}=\frac{b}{c}$ . When you divide both sides of an equation by any non-zero number, you still have equality. • The Multiplication Property of Equality —For any numbers a , b , and c , if $a=b$ , then $ac=bc$ . If you multiply both sides of an equation by the same number, you still have equality. Practice makes perfect Solve Equations Using the Division and Multiplication Properties of Equality In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. $8x=56$ $x=7$ $7p=63$ $-5c=55$ $c=-11$ $-9x=-27$ $-809=15y$ $y=-\frac{809}{15}$ $-731=19y$ $-37p=-541$ $p=-\frac{541}{37}$ $-19m=-586$ $0.25z=3.25$ $z=13$ $0.75a=11.25$ $-13x=0$ $x=0$ $24x=0$ $\frac{x}{4}=35$ $x=140$ $\frac{z}{2}=54$ $-20=\frac{q}{-5}$ $q=100$ $\frac{c}{-3}=-12$ $\frac{y}{9}=-16$ $y=-144$ $\frac{q}{6}=-38$ $\frac{m}{-12}=45$ $m=-540$ $-24=\frac{p}{-20}$ $\text{−}y=6$ $y=-6$ $\text{−}u=15$ $\text{−}v=-72$ $v=72$ $\text{−}x=-39$ $\frac{2}{3}y=48$ $y=72$ $\frac{3}{5}r=75$ $-\frac{5}{8}w=40$ $w=-64$ $24=-\frac{3}{4}x$ $-\frac{2}{5}=\frac{1}{10}a$ $a=-4$ $-\frac{1}{3}q=-\frac{5}{6}$ $-\frac{7}{10}x=-\frac{14}{3}$ $x=\frac{20}{3}$ $\frac{3}{8}y=-\frac{1}{4}$ $\frac{7}{12}=-\frac{3}{4}p$ $p=-\frac{7}{9}$ $\frac{11}{18}=-\frac{5}{6}q$ $-\frac{5}{18}=-\frac{10}{9}u$ $u=\frac{1}{4}$ $-\frac{7}{20}=-\frac{7}{4}v$ Solve Equations That Require Simplification In the following exercises, solve each equation requiring simplification. $100-16=4p-10p-p$ $p=-12$ $-18-7=5t-9t-6t$ $\frac{7}{8}n-\frac{3}{4}n=9+2$ $n=88$ $\frac{5}{12}q+\frac{1}{2}q=25-3$ $0.25d+0.10d=6-0.75$ $d=15$ $0.05p-0.01p=2+0.24$ $-10\left(q-4\right)-57=93$ $q=-11$ $-12\left(d-5\right)-29=43$ $-10\left(x+4\right)-19=85$ $x=-\frac{72}{5}$ $-15\left(z+9\right)-11=75$ Mixed Practice In the following exercises, solve each equation. $\frac{9}{10}x=90$ $x=100$ $\frac{5}{12}y=60$ $y+46=55$ $y=9$ $x+33=41$ $\frac{w}{-2}=99$ $w=-198$ $\frac{s}{-3}=-60$ $27=6a$ $a=\frac{9}{2}$ $\text{−}a=7$ $\text{−}x=2$ $x=-2$ $z-16=-59$ $m-41=-14$ $m=27$ $0.04r=52.60$ $63.90=0.03p$ $p=2130$ $-15x=-120$ $84=-12z$ $y=-7$ $19.36=x-0.2x$ $c-0.3c=35.70$ $c=51$ $\text{−}y=-9$ $\text{−}x=-8$ $x=8$ Translate to an Equation and Solve In the following exercises, translate to an equation and then solve. 187 is the product of $-17$ and m . 133 is the product of $-19$ and n . $133=-19n;n=-7$ $-184$ is the product of 23 and p . $-152$ is the product of 8 and q . $-152=8q;q=-19$ u divided by 7 is equal to $-49$ . r divided by 12 is equal to $-48$ . $\frac{r}{12}=-48;r=-576$ h divided by $-13$ is equal to $-65$ . j divided by $-20$ is equal to $-80$ . $\frac{j}{-20}=-80;j=1,600$ The quotient $c$ and $-19$ is 38. The quotient of $b$ and $-6$ is 18. $\frac{b}{-6}=18;b=-108$ The quotient of $h$ and 26 is $-52$ . The quotient $k$ and 22 is $-66$ . $\frac{k}{22}=-66;k=-1,452$ Five-sixths of y is 15. Three-tenths of x is 15. $\frac{3}{10}x=15;x=50$ Four-thirds of w is 36. Five-halves of v is 50. $\frac{5}{2}v=50;v=20$ The sum of nine-tenths and g is two-thirds. The sum of two-fifths and f is one-half. $\frac{2}{5}+f=\frac{1}{2};f=\frac{1}{10}$ The difference of p and one-sixth is two-thirds. The difference of q and one-eighth is three-fourths. $q-\frac{1}{8}=\frac{3}{4};q=\frac{7}{8}$ Translate and Solve Applications In the following exercises, translate into an equation and solve. Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group? Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. How many balloons did she use in each bunch? 6 balloons Tickets Mollie paid$36.25 for 5 movie tickets. What was the price of each ticket?

Shopping Serena paid $12.96 for a pack of 12 pairs of sport socks. What was the price of pair of sport socks?$1.08

Sewing Nancy used 14 yards of fabric to make flags for one-third of the drill team. How much fabric, would Nancy need to make flags for the whole team?

MPG John’s SUV gets 18 miles per gallon (mpg). This is half as many mpg as his wife’s hybrid car. How many miles per gallon does the hybrid car get?

36 mpg

Height Aiden is 27 inches tall. He is $\frac{3}{8}$ as tall as his father. How tall is his father?

Real estate Bea earned $11,700 commission for selling a house, calculated as $\frac{6}{100}$ of the selling price. What was the selling price of the house?$195,000

Everyday math

Commission Every week Perry gets paid $150 plus 12% of his total sales amount. Solve the equation $840=150+0.12\left(a-1250\right)$ for a , to find the total amount Perry must sell in order to be paid$840 one week.

Stamps Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation $0.49s+0.21\text{​}\left(s-5\right)\text{​}\text{​}=9.45$ for s , to find the number of 49-cent stamps Travis bought. 15 49-cent stamps Writing exercises Frida started to solve the equation $-3x=36$ by adding 3 to both sides. Explain why Frida’s method will not solve the equation. Emiliano thinks $x=40$ is the solution to the equation $\frac{1}{2}x=80$ . Explain why he is wrong. Answers will vary. Self check After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. What does this checklist tell you about your mastery of this section? What steps will you take to improve? Questions & Answers 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 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 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 Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs$6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs$5.71 per gallon?
(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
4x-7y=8 2x-7y=1 what is the answer?
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Frank
thanks
Ramil
copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x
What is c+4=8
2
Letha
4
Lolita
4
Rich
4
thinking
C+4=8 -4 -4 C =4
thinking
I need to study
Letha
4+4=8
William
During two years in college, a student earned $9,500. The second year, she earned$500 more than twice the amount she earned the first year.
9500=500+2x
Debra
9500-500=9000 9000÷2×=4500 X=4500
Debra
X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500
Pbp