Question

distributive property
solving equations using the distributive property
the distributive property allows us to remove the parentheses by distributing the value outside
the parentheses with each term located inside the parentheses. the distributive property is a
way to write an expression in expanded form.
example: 3(6 + 9)
there are two
terms inside the parentheses.
multiply the 3 by each term
inside the parentheses.
3 x 6 + 3 x 9
rewrite
18 + 27 = 45
solve
whenever a number is being multiplied by each term inside a set of parentheses it should be
recognized as the distributive property. the distributive property is necessary to solve some
algebraic equations or to simplify some algebraic expressions.
example: solve 5(x - 8) = 10
a)
b) 5x - 40 = 10
c)
d) x = 10
directions: find the value of x for each of the following equations.

1. 6(x + 3) = 48
2. 4(5 - x) = 8
3. 7(x + 2) + 3 = 73
4. 8(x - 3) = 96

1. 9(x + 3) = 27
2. 12(x + 20) = 372
3. 4(x - 5) = 44
4. 3(x - 20) = 15

1. 5(x + 9) - 4 = 51
2. 8(x + 100) - 3 = 837
3. 2(x - 5 + 2) = 6
4. 20(x + 1) = 200

1. 12(x - 4) = 144
2. 9(x + 9) = 90
3. 7(2 + x) = 35
4. 8(11 - x) = 16

Explanation:

1) Step1: Apply distributive property

$6x + 18 = 48$

1) Step2: Subtract 18 from both sides

$6x = 48 - 18$
$6x = 30$

1) Step3: Divide by 6

$x = \frac{30}{6}$
---

2) Step1: Apply distributive property

$20 - 4x = 8$

2) Step2: Subtract 20 from both sides

$-4x = 8 - 20$
$-4x = -12$

2) Step3: Divide by -4

$x = \frac{-12}{-4}$
---

3) Step1: Apply distributive property

$7x + 14 + 3 = 73$

3) Step2: Combine like terms

$7x + 17 = 73$

3) Step3: Subtract 17 from both sides

$7x = 73 - 17$
$7x = 56$

3) Step4: Divide by 7

$x = \frac{56}{7}$
---

4) Step1: Apply distributive property

$8x - 24 = 96$

4) Step2: Add 24 to both sides

$8x = 96 + 24$
$8x = 120$

4) Step3: Divide by 8

$x = \frac{120}{8}$
---

5) Step1: Apply distributive property

$9x + 27 = 27$

5) Step2: Subtract 27 from both sides

$9x = 27 - 27$
$9x = 0$

5) Step3: Divide by 9

$x = \frac{0}{9}$
---

6) Step1: Apply distributive property

$12x + 240 = 372$

6) Step2: Subtract 240 from both sides

$12x = 372 - 240$
$12x = 132$

6) Step3: Divide by 12

$x = \frac{132}{12}$
---

7) Step1: Apply distributive property

$4x - 20 = 44$

7) Step2: Add 20 to both sides

$4x = 44 + 20$
$4x = 64$

7) Step3: Divide by 4

$x = \frac{64}{4}$
---

8) Step1: Apply distributive property

$3x - 60 = 15$

8) Step2: Add 60 to both sides

$3x = 15 + 60$
$3x = 75$

8) Step3: Divide by 3

$x = \frac{75}{3}$
---

9) Step1: Apply distributive property

$5x + 45 - 4 = 51$

9) Step2: Combine like terms

$5x + 41 = 51$

9) Step3: Subtract 41 from both sides

$5x = 51 - 41$
$5x = 10$

9) Step4: Divide by 5

$x = \frac{10}{5}$
---

10) Step1: Apply distributive property

$8x + 800 - 3 = 837$

10) Step2: Combine like terms

$8x + 797 = 837$

10) Step3: Subtract 797 from both sides

$8x = 837 - 797$
$8x = 40$

10) Step4: Divide by 8

$x = \frac{40}{8}$
---

11) Step1: Simplify inside parentheses

$2(x - 3) = 6$

11) Step2: Apply distributive property

$2x - 6 = 6$

11) Step3: Add 6 to both sides

$2x = 6 + 6$
$2x = 12$

11) Step4: Divide by 2

$x = \frac{12}{2}$
---

12) Step1: Apply distributive property

$20x + 20 = 200$

12) Step2: Subtract 20 from both sides

$20x = 200 - 20$
$20x = 180$

12) Step3: Divide by 20

$x = \frac{180}{20}$
---

13) Step1: Apply distributive property

$12x - 48 = 144$

13) Step2: Add 48 to both sides

$12x = 144 + 48$
$12x = 192$

13) Step3: Divide by 12

$x = \frac{192}{12}$
---

14) Step1: Apply distributive property

$9x + 81 = 90$

14) Step2: Subtract 81 from both sides

$9x = 90 - 81$
$9x = 9$

14) Step3: Divide by 9

$x = \frac{9}{9}$
---

15) Step1: Apply distributive property

$14 + 7x = 35$

15) Step2: Subtract 14 from both sides

$7x = 35 - 14$
$7x = 21$

15) Step3: Divide by 7

$x = \frac{21}{7}$
---

16) Step1: Apply distributive property

$88 - 8x = 16$

16) Step2: Subtract 88 from both sides

$-8x = 16 - 88$
$-8x = -72$

16) Step3: Divide by -8

$x = \frac{-72}{-8}$

Answer:

1. $x = 5$
2. $x = 3$
3. $x = 8$
4. $x = 15$
5. $x = 0$
6. $x = 11$
7. $x = 16$
8. $x = 25$
9. $x = 2$
10. $x = 5$
11. $x = 6$
12. $x = 9$
13. $x = 16$
14. $x = 1$
15. $x = 3$
16. $x = 9$