Question

show work to solve the equation. then check your solution.

1. $18 + m = 25$ 21. $x + 36 = 42$ 22. $18 - s = 11$
2. $p - 11 = 12$ 24. $9y = 54$ 25. $\frac{40}{b} = 10$
3. $15n = 45$ 27. $\frac{x}{5} = 7$ 28. $\frac{r}{4} = 8$
4. $p - 17 = 18$ 30. $n + 12 = 21$ 31. $2m = 28$

5.2 writing equations

Explanation:

20. Step1: Isolate $m$ by subtracting 18

$18 + m - 18 = 25 - 18$

20. Step2: Simplify to find $m$

$m = 7$

20. Step3: Check solution

$18 + 7 = 25$, $25=25$ (valid)

21. Step1: Isolate $x$ by subtracting 36

$x + 36 - 36 = 42 - 36$

21. Step2: Simplify to find $x$

$x = 6$

21. Step3: Check solution

$6 + 36 = 42$, $42=42$ (valid)

22. Step1: Isolate $-s$ by subtracting 18

$18 - s - 18 = 11 - 18$

22. Step2: Simplify and solve for $s$

$-s = -7 \implies s=7$

22. Step3: Check solution

$18 - 7 = 11$, $11=11$ (valid)

23. Step1: Isolate $p$ by adding 11

$p - 11 + 11 = 12 + 11$

23. Step2: Simplify to find $p$

$p = 23$

23. Step3: Check solution

$23 - 11 = 12$, $12=12$ (valid)

24. Step1: Isolate $y$ by dividing by 9

$\frac{9y}{9} = \frac{54}{9}$

24. Step2: Simplify to find $y$

$y = 6$

24. Step3: Check solution

$9 \times 6 = 54$, $54=54$ (valid)

25. Step1: Multiply both sides by $b$

$b \times \frac{40}{b} = 10 \times b$

25. Step2: Isolate $b$ by dividing by 10

$\frac{40}{10} = \frac{10b}{10}$

25. Step3: Simplify to find $b$

$b = 4$

25. Step4: Check solution

$\frac{40}{4} = 10$, $10=10$ (valid)

26. Step1: Isolate $n$ by dividing by 15

$\frac{15n}{15} = \frac{45}{15}$

26. Step2: Simplify to find $n$

$n = 3$

26. Step3: Check solution

$15 \times 3 = 45$, $45=45$ (valid)

27. Step1: Isolate $x$ by multiplying by 5

$\frac{x}{5} \times 5 = 7 \times 5$

27. Step2: Simplify to find $x$

$x = 35$

27. Step3: Check solution

$\frac{35}{5} = 7$, $7=7$ (valid)

28. Step1: Isolate $r$ by multiplying by 4

$\frac{r}{4} \times 4 = 8 \times 4$

28. Step2: Simplify to find $r$

$r = 32$

28. Step3: Check solution

$\frac{32}{4} = 8$, $8=8$ (valid)

29. Step1: Isolate $p$ by adding 17

$p - 17 + 17 = 18 + 17$

29. Step2: Simplify to find $p$

$p = 35$

29. Step3: Check solution

$35 - 17 = 18$, $18=18$ (valid)

30. Step1: Isolate $n$ by subtracting 12

$n + 12 - 12 = 21 - 12$

30. Step2: Simplify to find $n$

$n = 9$

30. Step3: Check solution

$9 + 12 = 21$, $21=21$ (valid)

31. Step1: Isolate $m$ by dividing by 2

$\frac{2m}{2} = \frac{28}{2}$

31. Step2: Simplify to find $m$

$m = 14$

31. Step3: Check solution

$2 \times 14 = 28$, $28=28$ (valid)

Answer:

1. $m=7$
2. $x=6$
3. $s=7$
4. $p=23$
5. $y=6$
6. $b=4$
7. $n=3$
8. $x=35$
9. $r=32$
10. $p=35$
11. $n=9$
12. $m=14$