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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