SOLVING MULTI STEP EQUATIONS

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.

Solving multi step equations - Examples

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

After having gone through the stuff given above, we hope that the students would have understood "Solving multi step equations".

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