SOLVING MULTI STEP EQUATIONS

In solving multi step equations, we will be using more than one binary operation to get value of the variable or unknown.

Example 1 : 

Solve for x : 

3x + 5  =  11

Solution :

Step 1 :

3x + 5  =  11

To get rid of 5, subtract 5 on both sides of the equation. 

(3x + 5) - 5  =  11 - 5

3x  =  6

Step 2 :

3x  =  6

To get rid of 3, divide both sides of the equation by 3.

3x / 3  =  6/3

x  =  2

Example 2 : 

Solve for x : 

(1/3)x - 1  =  7

Solution : 

Step 1 : 

x/3 - 1  =  7

To get rid of -1, add 1 on both sides of the equation. 

[x/3 - 1] + 1  =  7 + 1

x/3  =  8

Step 2 : 

x/3  =  8

To get rid of 3, multiply both sides of the equation by 3.

3(x / 3)  =  3(8)

x  =  24

Example 3 : 

Solve for g : 

(g - 3) / 4  =  5

Solution : 

Step 1 : 

(g - 3) / 4  =  5

To get rid of 4, multiply both sides of the equation by 4.

4[(g - 3) / 4]  =  4(5)

g - 3  =  20

Step 2 : 

g - 3  =  20

To get rid of 3, add 3 on both sides of the equation. 

(g - 3) + 3  =  20 + 3

g  =  23

Example 4 : 

Solve for g : 

(g + 5)/3 + 2  =  0

Solution : 

Step 1 : 

(g + 5)/3 + 2  =  0

To get rid of 2, subtract 2 on both sides of the equation.

(g + 5)/3 + 2 - 2  =  0 - 2

(g + 5)/3  =  -2

Step 2 : 

(g + 5)/3  =  -2

To get rid of 3, multiply both sides of the equation by 3.

3[(g + 5) / 3]  =  3(-2)

g + 5  =  -6

Step 3 : 

g + 5  =  -6

To get rid of 5, subtract 5 on both sides of the equation. 

(g + 5) - 5  =  -6 - 5

g  =  -11

Example 5 : 

Solve for g : 

(5g + 8)/7 - 9  =  0

Solution : 

Step 1 : 

(5g + 8)/7 - 9  =  0

To get rid of 9, add 9 on both sides of the equation.

(5g + 8)/7 - 9 + 9  =  0 + 9

(5g + 8)/7  =  9

Step 2 : 

(5g + 8)/7  =  9

To get rid of 7, multiply both sides of the equation by 7.

7[(5g + 8)/7]  =  7(9)

5g + 8  =  63

Step 3 : 

5g + 8  =  63

To get rid of 8, subtract 8 on both sides of the equation. 

(5g + 8) - 8  =  63 - 8

5g  =  55

Step 4 : 

5g  =  55

To get rid of 5, divide both sides of the equation by 5. 

5g / 5  =  55 / 5

g  =  11

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