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Solve an Equation with Constants on Both Sides
In the following exercises, solve the equation for the variable.
$6x-2=40$
$11w+6=93$
$3a+8=\mathrm{-46}$
$\mathrm{-50}=7n-1$
$25=\mathrm{-9}y+7$
$\mathrm{-12}p-3=15$
Solve an Equation with Variables on Both Sides
In the following exercises, solve the equation for the variable.
$8z=7z-7$
$4x+36=10x$
$c=\mathrm{-3}c-20$
$5q=44-6q$
$3y+\frac{1}{2}=2y$
$\mathrm{-12}a-8=\mathrm{-16}a$
Solve an Equation with Variables and Constants on Both Sides
In the following exercises, solve the equations for the variable.
$6x-15=5x+3$
$26+8d=9d+11$
$3p-1=5p-33$
$4a+5=-a-40$
$8y-30=\mathrm{-2}y+30$
$2\text{z}-4=23-\text{z}$
$\frac{5}{4}\phantom{\rule{0.1em}{0ex}}c-3=\frac{1}{4}\phantom{\rule{0.1em}{0ex}}c-16$
$\frac{4}{3}\phantom{\rule{0.1em}{0ex}}m-7=\frac{1}{3}\phantom{\rule{0.1em}{0ex}}m-13$
6
$8-\frac{2}{5}\phantom{\rule{0.1em}{0ex}}q=\frac{3}{5}\phantom{\rule{0.1em}{0ex}}q+6$
$11-\frac{1}{4}\phantom{\rule{0.1em}{0ex}}a=\frac{3}{4}\phantom{\rule{0.1em}{0ex}}a+4$
7
$\frac{4}{3}\phantom{\rule{0.1em}{0ex}}n+9=\frac{1}{3}\phantom{\rule{0.1em}{0ex}}n-9$
$\frac{5}{4}\phantom{\rule{0.1em}{0ex}}a+15=\frac{3}{4}\phantom{\rule{0.1em}{0ex}}a-5$
−40
$\frac{1}{4}\phantom{\rule{0.1em}{0ex}}y+7=\frac{3}{4}\phantom{\rule{0.1em}{0ex}}y-3$
$\frac{3}{5}\phantom{\rule{0.1em}{0ex}}p+2=\frac{4}{5}\phantom{\rule{0.1em}{0ex}}p-1$
3
$14n+8.25=9n+19.60$
$2.4w-100=0.8w+28$
$5.6r+13.1=3.5r+57.2$
Solve an Equation Using the General Strategy
In the following exercises, solve the linear equation using the general strategy.
$5(x+3)=75$
$8=4(x-3)$
$20(y-8)=\mathrm{-60}$
$\mathrm{-4}(2n+1)=16$
$3(10+5r)=0$
$\frac{2}{3}(9c-3)=22$
$5(1.2u-4.8)=\mathrm{-12}$
$0.2(30n+50)=28$
$-(w-6)=24$
$9(3a+5)+9=54$
$10+3(z+4)=19$
$7+5(4-q)=12$
$15-(3r+8)=28$
$11-4(y-8)=43$
$9(p-1)=6(2p-1)$
$9(2m-3)-8=4m+7$
$8(x-4)-7x=14$
$\mathrm{-12}+8(x-5)=\mathrm{-4}+3(5x-2)$
$7(2x-5)=8(4x-1)-9$
Making a fence Jovani has a fence around the rectangular garden in his backyard. The perimeter of the fence is $150$ feet. The length is $15$ feet more than the width. Find the width, $w,$ by solving the equation $150=2(w+15)+2w.$
30 feet
Concert tickets At a school concert, the total value of tickets sold was $\text{\$1,506.}$ Student tickets sold for $\text{\$6}$ and adult tickets sold for $\text{\$9.}$ The number of adult tickets sold was $5$ less than $3$ times the number of student tickets. Find the number of student tickets sold, $s,$ by solving the equation $6s+9(3s-5)=1506.$
Coins Rhonda has $\text{\$1.90}$ in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, $n,$ by solving the equation $0.05n+0.10(2n-1)=1.90.$
8 nickels
Fencing Micah has $74$ feet of fencing to make a rectangular dog pen in his yard. He wants the length to be $25$ feet more than the width. Find the length, $L,$ by solving the equation $2L+2(L-25)=74.$
When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient as the variable side?
Answers will vary.
Solve the equation $10x+14=\mathrm{-2}x+38,$ explaining all the steps of your solution.
What is the first step you take when solving the equation $3-7(y-4)=38?$ Explain why this is your first step.
Answers will vary.
Solve the equation $\frac{1}{4}(8x+20)=3x-4$ explaining all the steps of your solution as in the examples in this section.
Using your own words, list the steps in the General Strategy for Solving Linear Equations.
Answers will vary.
Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.
ⓐ 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?
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