EQUATIONS WITH DISTRIBUTIVE PROPERTY ON BOTH SIDES

In this section, you will learn how to solve equations using the distributive property on both sides of the equation.

Example 1 :

Solve for x :

4(x - 3)  =  3(2 + x)

Solution :

Step 1 : 

Use the Distributive Property.

Distribute 4 to the terms inside the parentheses on the left side and 3 to the terms inside parentheses on the right side.

4x - 12  =  6 + 3x

Step 2 : 

Use inverse operations to solve the equation.

4x - 12  =  6 + 3x

Subtract 3x from each side. 

x - 12  =  6

Add 12 to each side. 

x  =  18

Example 2 :

Solve for x :

(3/4)(x - 13)  =  -2(9 + x)

Solution :

Step 1 : 

(3/4)(x - 13)  =  -2(9 + x)

Multiply both sides of the equation by 4 to get rid of the denominator 4 on the left side. 

3(x - 13)  =  -8(9 + x)

Step 2 : 

Use the distributive property. 

3x - 39  =  -72 - 8x

Step 3 : 

Use inverse operations to solve the equation.

3x - 39  =  -72 - 8x

Add 8x to each side. 

11x - 39  =  -72

Add 39 to each side.  

11x  =  -33

Divide each side by 11.

x  =  -3

Example 3 :

Solve for b :

-4(-5 - b)  =  (1/3)(b + 16)

Solution :

Step 1 : 

-4(-5 - b)  =  (1/3)(b + 16)

Multiply both sides of the equation by 3 to get rid of the denominator 3 on the right side. 

-12(-5 - b)  =  1(b + 16)

Step 2 : 

Use the distributive property. 

60 + 12b  =  b + 16

Step 3 : 

Use inverse operations to solve the equation.

60 + 12b  =  b + 16

Subtract b from each side. 

60 + 11b  =  16

Subtract 60 from each side. 

11b  =  -44

Divide each side by 11.

b  =  -4

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