Question

solve multi-step equations additional practice

1. 6x - 15 = 81
2. 3(8x + 6) = 30
3. 3(8x + 2) = 162
4. 30 = -4x - 6x
5. 4x + 6 + 3 = 17
6. 4x + 9 = 2x - 6
7. 3x + 7 = x - 15
8. 7x + 2(x + 6) = 39
9. 4x + 2x - 3x = 27
10. 16 = 2(x - 1) - x

Explanation:

1) Step1: Isolate the variable term

$4x = 15 - 8$

1) Step2: Simplify right-hand side

$4x = 7$

1) Step3: Solve for $x$

$x = \frac{7}{4}$

2) Step1: Divide both sides by 3

$8x + 2 = \frac{162}{3}$

2) Step2: Simplify right-hand side

$8x + 2 = 54$

2) Step3: Isolate the variable term

$8x = 54 - 2$

2) Step4: Simplify right-hand side

$8x = 52$

2) Step5: Solve for $x$

$x = \frac{52}{8} = \frac{13}{2}$

3) Step1: Combine constant terms

$4x + 9 = 17$

3) Step2: Isolate the variable term

$4x = 17 - 9$

3) Step3: Simplify right-hand side

$4x = 8$

3) Step4: Solve for $x$

$x = \frac{8}{4} = 2$

4) Step1: Group variable terms

$3x - x = -15 - 7$

4) Step2: Simplify both sides

$2x = -22$

4) Step3: Solve for $x$

$x = \frac{-22}{2} = -11$

5) Step1: Combine like terms

$(4+2-3)x = 27$

5) Step2: Simplify coefficient

$3x = 27$

5) Step3: Solve for $x$

$x = \frac{27}{3} = 9$

6) Step1: Divide both sides by 3

$6x + 6 = \frac{39}{3}$

6) Step2: Simplify right-hand side

$6x + 6 = 13$

6) Step3: Isolate the variable term

$6x = 13 - 6$

6) Step4: Simplify right-hand side

$6x = 7$

6) Step5: Solve for $x$

$x = \frac{7}{6}$

7) Step1: Combine variable terms

$39 = (-4-6)x$

7) Step2: Simplify coefficient

$39 = -10x$

7) Step3: Solve for $x$

$x = \frac{39}{-10} = -\frac{39}{10}$

8) Step1: Group variable terms

$4x - 2x = -6 - 9$

8) Step2: Simplify both sides

$2x = -15$

8) Step3: Solve for $x$

$x = -\frac{15}{2}$

9) Step1: Expand the parentheses

$7x + 2x + 12 = 39$

9) Step2: Combine like terms

$9x + 12 = 39$

9) Step3: Isolate the variable term

$9x = 39 - 12$

9) Step4: Simplify right-hand side

$9x = 27$

9) Step5: Solve for $x$

$x = \frac{27}{9} = 3$

10) Step1: Expand the parentheses

$16 = 2x - 2 - x$

10) Step2: Combine like terms

$16 = x - 2$

10) Step3: Isolate $x$

$x = 16 + 2$

10) Step4: Simplify right-hand side

$x = 18$

Answer:

1. $x=\frac{7}{4}$
2. $x=\frac{13}{2}$
3. $x=2$
4. $x=-11$
5. $x=9$
6. $x=\frac{7}{6}$
7. $x=-\frac{39}{10}$
8. $x=-\frac{15}{2}$
9. $x=3$
10. $x=18$