Question

solve the equation.

1. $2c - 5 = 9$ 2. $3m + 7 = -8$
2. $-7x - 3 = 12$ 4. $15 = 4a + 3$
3. $5y - 6 = -20$ 6. $9f + 3.6 = 10.8$
4. $-4p - 5.7 = 11.1$ 8. $-20.3 = 6w + 3.1$
5. $2 + 5.3k = 18.43$ 10. $7.8b - 2.14 = -42.7$
6. $\frac{1}{4}z - \frac{2}{7} = \frac{5}{7}$ 12. $3 - \frac{r}{8} = -\frac{9}{2}$
7. $-\frac{1}{3} + 5e = -\frac{3}{4}$ 14. $14d - 2d = -84$
8. $-5g - 13g = 54$ 16. $-3(t - 8) = 32$
9. kayla’s age is 3 less than twice her brother’s age. kayla is 13 years old. how old is her brother?
10. mario spent $23.85 at the bookstore on one book and some magazines. the book cost $12.60 and the magazines cost $2.25 each. how many magazines did mario buy?
11. ethan planted a tree that is 37.5 inches tall. if the tree grows 3 inches each year, how long will it take for the tree to reach a height of 54 inches?

Explanation:

Step1: Isolate term with $c$

Add 5 to both sides:
$2c - 5 + 5 = 9 + 5$
$2c = 14$

Step2: Solve for $c$

Divide by 2:
$c = \frac{14}{2} = 7$

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Step1: Isolate term with $m$

Subtract 7 from both sides:
$3m + 7 - 7 = -8 - 7$
$3m = -15$

Step2: Solve for $m$

Divide by 3:
$m = \frac{-15}{3} = -5$

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Step1: Isolate term with $x$

Add 3 to both sides:
$-7x - 3 + 3 = 12 + 3$
$-7x = 15$

Step2: Solve for $x$

Divide by -7:
$x = -\frac{15}{7}$

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Step1: Isolate term with $a$

Subtract 3 from both sides:
$15 - 3 = 4a + 3 - 3$
$12 = 4a$

Step2: Solve for $a$

Divide by 4:
$a = \frac{12}{4} = 3$

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Step1: Isolate term with $y$

Add 6 to both sides:
$5y - 6 + 6 = -20 + 6$
$5y = -14$

Step2: Solve for $y$

Divide by 5:
$y = -\frac{14}{5} = -2.8$

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Step1: Isolate term with $f$

Subtract 3.6 from both sides:
$9f + 3.6 - 3.6 = 10.8 - 3.6$
$9f = 7.2$

Step2: Solve for $f$

Divide by 9:
$f = \frac{7.2}{9} = 0.8$

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Step1: Isolate term with $p$

Add 5.7 to both sides:
$-4p - 5.7 + 5.7 = 11.1 + 5.7$
$-4p = 16.8$

Step2: Solve for $p$

Divide by -4:
$p = \frac{16.8}{-4} = -4.2$

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Step1: Isolate term with $w$

Subtract 3.1 from both sides:
$-20.3 - 3.1 = 6w + 3.1 - 3.1$
$-23.4 = 6w$

Step2: Solve for $w$

Divide by 6:
$w = \frac{-23.4}{6} = -3.9$

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Step1: Isolate term with $k$

Subtract 2 from both sides:
$2 + 5.3k - 2 = 18.43 - 2$
$5.3k = 16.43$

Step2: Solve for $k$

Divide by 5.3:
$k = \frac{16.43}{5.3} = 3.1$

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Step1: Isolate term with $b$

Add 2.14 to both sides:
$7.8b - 2.14 + 2.14 = -42.7 + 2.14$
$7.8b = -40.56$

Step2: Solve for $b$

Divide by 7.8:
$b = \frac{-40.56}{7.8} = -5.2$

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Step1: Isolate term with $z$

Add $\frac{2}{7}$ to both sides:
$\frac{1}{4}z - \frac{2}{7} + \frac{2}{7} = \frac{5}{7} + \frac{2}{7}$
$\frac{1}{4}z = 1$

Step2: Solve for $z$

Multiply by 4:
$z = 1 \times 4 = 4$

---

Step1: Isolate term with $r$

Subtract 3 from both sides:
$3 - \frac{r}{8} - 3 = -\frac{9}{2} - 3$
$-\frac{r}{8} = -\frac{9}{2} - \frac{6}{2} = -\frac{15}{2}$

Step2: Solve for $r$

Multiply by -8:
$r = -\frac{15}{2} \times (-8) = 60$

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Step1: Isolate term with $e$

Add $\frac{1}{3}$ to both sides:
$-\frac{1}{3} + 5e + \frac{1}{3} = -\frac{3}{4} + \frac{1}{3}$
$5e = -\frac{9}{12} + \frac{4}{12} = -\frac{5}{12}$

Step2: Solve for $e$

Divide by 5:
$e = -\frac{5}{12} \times \frac{1}{5} = -\frac{1}{12}$

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Step1: Combine like terms

$14d - 2d = 12d$
$12d = -84$

Step2: Solve for $d$

Divide by 12:
$d = \frac{-84}{12} = -7$

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Step1: Combine like terms

$-5g - 13g = -18g$
$-18g = 54$

Step2: Solve for $g$

Divide by -18:
$g = \frac{54}{-18} = -3$

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Step1: Distribute the -3

$-3(t - 8) = -3t + 24 = 32$

Step2: Isolate term with $t$

Subtract 24 from both sides:
$-3t + 24 - 24 = 32 - 24$
$-3t = 8$

Step3: Solve for $t$

Divide by -3:
$t = -\frac{8}{3}$

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Step1: Define variable, set up equation

Let $b$ = brother's age. Equation: $2b - 3 = 13$

Step2: Isolate term with $b$

Add 3 to both sides:
$2b - 3 + 3 = 13 + 3$
$2b = 16$

Step3: Solve for $b$

Divide by 2:
$b = \frac{16}{2} = 8$

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Step1: Define variable, set up equation

Let $m$ = number of magazines. Equation: $12.60 + 2.25m = 23.85$

Step2: Isolate term with $m$

Subtract 12.60:
$2.25m = 23.85 - 12.60 = 11.25$

Step3: Solve for $m$

Divide by 2.25:
$m = \frac{11.25}{2.25} = 5$

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Step1: Define variable, set up equation

Let $t$ = time in years. Equation: $37.5 + 3t = 54$

Step2: Isolate term with $t$

Subtract 37.5:
$3t = 54 - 37.5 = 16.5$

Step3: Solve for $t$

Divide by 3:
$t = \frac{16.5}{3} = 5.5$

Answer:

1. $c=7$
2. $m=-5$
3. $x=-\frac{15}{7}$
4. $a=3$
5. $y=-2.8$
6. $f=0.8$
7. $p=-4.2$
8. $w=-3.9$
9. $k=3.1$
10. $b=-5.2$
11. $z=4$
12. $r=60$
13. $e=-\frac{1}{12}$
14. $d=-7$
15. $g=-3$
16. $t=-\frac{8}{3}$
17. 8 years old
18. 5 magazines
19. 5.5 years