2.3E: Exercises

Practice Makes Perfect

Solve Equations with Constants on Both Sides

In the following exercises, solve the following equations with constants on both sides.

Exercise $\PageIndex{1}$

$9 x-3=60$

Exercise $\PageIndex{2}$

$12 x-8=64$

Answer

$x=6$

Exercise $\PageIndex{3}$

$14 w+5=117$

Exercise $\PageIndex{4}$

$15 y+7=97$

Answer

$y=6$

Exercise $\PageIndex{5}$

$2 a+8=-28$

Exercise $\PageIndex{6}$

$3 m+9=-15$

Answer

$m=-8$

Exercise $\PageIndex{7}$

$-62=8 n-6$

Exercise $\PageIndex{8}$

$-77=9 b-5$

Answer

$b=-8$

Exercise $\PageIndex{9}$

$35=-13 y+9$

Exercise $\PageIndex{10}$

$60=-21 x-24$

Answer

$x=-4$

Exercise $\PageIndex{11}$

$-12 p-9=9$

Exercise $\PageIndex{12}$

$-14 q-2=16$

Answer

$q=-\frac{9}{7}$

Solve Equations with Variables on Both Sides

In the following exercises, solve the following equations with variables on both sides.

Exercise $\PageIndex{13}$

$19 z=18 z-7$

Exercise $\PageIndex{14}$

$21 k=20 k-11$

Answer

$k=-11$

Exercise $\PageIndex{15}$

$9 x+36=15 x$

Exercise $\PageIndex{16}$

$8 x+27=11 x$

Answer

$x=9$

Exercise $\PageIndex{17}$

$c=-3 c-20$

Exercise $\PageIndex{18}$

$b=-4 b-15$

Answer

$b=-3$

Exercise $\PageIndex{19}$

$9 q=44-2 q$

Exercise $\PageIndex{20}$

$5 z=39-8 z$

Answer

$z=3$

Exercise $\PageIndex{21}$

$6 y+\frac{1}{2}=5 y$

Exercise $\PageIndex{22}$

$4 x+\frac{3}{4}=3 x$

Answer

$x=-\frac{3}{4}$

Exercise $\PageIndex{23}$

$-18 a-8=-22 a$

Exercise $\PageIndex{24}$

$-11 r-8=-7 r$

Answer

$r=-2$

Solve Equations with Variables and Constants on Both Sides

In the following exercises, solve the following equations with variables and constants on both sides.

Exercise $\PageIndex{25}$

$8 x-15=7 x+3$

Exercise $\PageIndex{26}$

$6 x-17=5 x+2$

Answer

$x=19$

Exercise $\PageIndex{27}$

$26+13 d=14 d+11$

Exercise $\PageIndex{28}$

$21+18 f=19 f+14$

Answer

$f=7$

Exercise $\PageIndex{29}$

$2 p-1=4 p-33$

Exercise $\PageIndex{30}$

$12 q-5=9 q-20$

Answer

$q=-5$

Exercise $\PageIndex{31}$

$4 a+5=-a-40$

Exercise $\PageIndex{32}$

$8 c+7=-3 c-37$

Answer

$c=-4$

Exercise $\PageIndex{33}$

$5 y-30=-5 y+30$

Exercise $\PageIndex{34}$

$7 x-17=-8 x+13$

Answer

$x=2$

Exercise $\PageIndex{35}$

$7 s+12=5+4 s$

Exercise $\PageIndex{36}$

$9 p+14=6+4 p$

Answer

$p=-\frac{8}{5}$

Exercise $\PageIndex{37}$

$2 z-6=23-z$

Exercise $\PageIndex{38}$

$3 y-4=12-y$

Answer

$y=4$

Exercise $\PageIndex{39}$

$\frac{5}{3} c-3=\frac{2}{3} c-16$

Exercise $\PageIndex{40}$

$\frac{7}{4} m-7=\frac{3}{4} m-13$

Answer

$m=-6$

Exercise $\PageIndex{41}$

$8-\frac{2}{5} q=\frac{3}{5} q+6$

Exercise $\PageIndex{42}$

$11-\frac{1}{5} a=\frac{4}{5} a+4$

Answer

$a=7$

Exercise $\PageIndex{43}$

$\frac{4}{3} n+9=\frac{1}{3} n-9$

Exercise $\PageIndex{44}$

$\frac{5}{4} a+15=\frac{3}{4} a-5$

Answer

$a=-40$

Exercise $\PageIndex{45}$

$\frac{1}{4} y+7=\frac{3}{4} y-3$

Exercise $\PageIndex{46}$

$\frac{3}{5} p+2=\frac{4}{5} p-1$

Answer

$p=15$

Exercise $\PageIndex{47}$

$14 n+8.25=9 n+19.60$

Exercise $\PageIndex{48}$

$13 z+6.45=8 z+23.75$

Answer

$z=3.46$

Exercise $\PageIndex{49}$

$2.4 w-100=0.8 w+28$

Exercise $\PageIndex{50}$

$2.7 w-80=1.2 w+10$

Answer

$w=60$

Exercise $\PageIndex{51}$

$5.6 r+13.1=3.5 r+57.2$

Exercise $\PageIndex{52}$

$6.6 x-18.9=3.4 x+54.7$

Answer

$x=23$

Everyday Math

Exercise $\PageIndex{53}$

Concert tickets At a school concert the total value of tickets sold was $1506. Student tickets sold for $6 and adult tickets sold for $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+27s−45=1506. Add exercises text here.

Exercise $\PageIndex{54}$

Making a fence Jovani has 150 feet of fencing to make a rectangular garden in his backyard. He wants the length to be 15
feet more than the width. Find the width, w, by solving the equation $150=2 w+30+2 w$.

Answer

30 feet

Writing Exercises

Exercise $\PageIndex{55}$

Solve the equation $\frac{6}{5} y-8=\frac{1}{5} y+7$ explaining all the steps of your solution as in the examples in this section.

Exercise $\PageIndex{56}$

Solve the equation $10 x+14=-2 x+38$ explaining all the steps of your solution as in this section.

Answer

$x=2$ Justifications will vary.

Exercise $\PageIndex{57}$

When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient
of $x$ to be the "variable" side?

Exercise $\PageIndex{58}$

Is $x=-2$ a solution to the equation $5-2 x=-4 x+1 ?$ How do you know?

Answer

Yes. Justifications 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?