Question

solving multi-step equations leveled practice
level 1: solve each one-step equation.

1. $7b = -126$
2. $-48 = -6k$
3. $\frac{r}{20} = -\frac{19}{20}$
4. $-146 = -20 + v$
5. $\frac{n}{8} = -6$
6. $2 = x + 8$

level 1 (entry): solve each 2-step equation.

1. $-190 = 72 + x$
2. $-7 = 3x + 8$
3. $22 = 6x - 7$
4. $-10x - 1 = -91$
5. $8(-5 + d) = 80$
6. $\frac{x}{5} + 2 = -1$

level 2: solve each multi-step equation.

1. $-6(-4x - 2) = -228$
2. $-201 = -3 + 6(-6x - 3)$

Explanation:

Step1: Solve 7b = -126

Divide both sides by 7:
$\frac{7b}{7} = \frac{-126}{7}$

Step2: Solve 46 = -d

Multiply both sides by -1:
$46 \times (-1) = -d \times (-1)$

Step3: Solve $\frac{r}{20} = \frac{30}{20}$

Multiply both sides by 20:
$\frac{r}{20} \times 20 = \frac{30}{20} \times 20$

Step4: Solve -14k = -28 + 7k

Subtract 7k from both sides:
$-14k -7k = -28 +7k -7k$
$\implies -21k = -28$
Divide by -21:
$\frac{-21k}{-21} = \frac{-28}{-21}$

Step5: Solve $\frac{h}{6} = -6$

Multiply both sides by 6:
$\frac{h}{6} \times 6 = -6 \times 6$

Step6: Solve 2 = x + 8

Subtract 8 from both sides:
$2 -8 = x +8 -8$

Step7: Solve -196 = 70 + x

Subtract 70 from both sides:
$-196 -70 = 70 +x -70$

Step8: Solve -7 = 3x + 8

Subtract 8 from both sides:
$-7 -8 = 3x +8 -8$
$\implies -15 = 3x$
Divide by 3:
$\frac{-15}{3} = \frac{3x}{3}$

Step9: Solve 22 = 6x -7

Add 7 to both sides:
$22 +7 = 6x -7 +7$
$\implies 29 = 6x$
Divide by 6:
$\frac{29}{6} = \frac{6x}{6}$

Step10: Solve -10x -1 = -51

Add 1 to both sides:
$-10x -1 +1 = -51 +1$
$\implies -10x = -50$
Divide by -10:
$\frac{-10x}{-10} = \frac{-50}{-10}$

Step11: Solve 8(-5 +v) = 48

Divide both sides by 8:
$\frac{8(-5 +v)}{8} = \frac{48}{8}$
$\implies -5 +v = 6$
Add 5 to both sides:
$-5 +v +5 = 6 +5$

Step12: Solve $\frac{x}{5} +2 = -1$

Subtract 2 from both sides:
$\frac{x}{5} +2 -2 = -1 -2$
$\implies \frac{x}{5} = -3$
Multiply by 5:
$\frac{x}{5} \times5 = -3 \times5$

Step13: Solve -6(-4x -2) = -228

Divide both sides by -6:
$\frac{-6(-4x -2)}{-6} = \frac{-228}{-6}$
$\implies -4x -2 = 38$
Add 2 to both sides:
$-4x -2 +2 = 38 +2$
$\implies -4x = 40$
Divide by -4:
$\frac{-4x}{-4} = \frac{40}{-4}$

Step14: Solve -201 = -3 +6(-6x -3)

Simplify the right-hand side:
$-201 = -3 +6(-6x) +6(-3)$
$\implies -201 = -3 -36x -18$
$\implies -201 = -21 -36x$
Add 21 to both sides:
$-201 +21 = -21 -36x +21$
$\implies -180 = -36x$
Divide by -36:
$\frac{-180}{-36} = \frac{-36x}{-36}$

Answer:

1. $b = -18$
2. $d = -46$
3. $r = 30$
4. $k = \frac{4}{3}$
5. $h = -36$
6. $x = -6$
7. $x = -266$
8. $x = -5$
9. $x = \frac{29}{6}$
10. $x = 5$
11. $v = 11$
12. $x = -15$
13. $x = -10$
14. $x = 5$