# USING SUBTRACTION TO SOLVE EQUATIONS

We can use subtraction to solve equations which contain addition.

That is, when an equation contains addition, solve by subtracting the same number from both sides.

## Subtraction Property of Equality

You can subtract number from both sides of an equation, and the two sides will remain equal.

Example 1 :

Solve the equation and graph the solution on a number line.

Solution :

a + 15 = 26

Since we are trying to solve for a, we have to get rid of 15 which is added to a.

To get rid of 15, we have to subtract 15 on both sides.

(a + 15) - 15 = 26 - 15

a + 15 - 15 = 11

a = 11

Example 2 :

Solve the equation and graph the solution on a number line.

Solution :

5 = w + 1.5

Subtract 1.5 from both sides.

5 - 1.5 = (w + 1.5) - 1.5

3.5 = w + 1.5 - 1.5

3.5 = w

Example 3 :

Solve for x :

x + 7 = 8

Solution :

x + 7 = 8

Subtract 7 from both sides.

(x + 7) - 7 = 8 - 7

x + 7 - 7 = 1

x = 1

Example 4 :

Solve for a :

a + 3 = 11

Solution :

a + 3 = 11

Subtract 3 from both sides.

(a + 3) - 3 = 11 - 3

a + 3 - 3 = 8

a = 8

Example 5 :

Adding 7 to a number results 25. Find the number.

Solution :

Let x be the number.

x + 7 = 25

Subtract 7 from both sides.

(x + 7) - 7 = (25) - 7

x + 7 - 7 = 18

x = 18

Example 6 :

The sum of two numbers is 22.5. If one number is 7.5, find the other number.

Solution :

Let x be the other number.

x + 7.5 = 22.5

Subtract 7.5 from both sides.

(x + 7.5) - 7.5 = 22.5 - 7.5

x + 7.5 - 7.5 = 15

x = 15

Example 7 :

A puppy weighed 6 ounces at birth. After two weeks, the puppy weighed 14 ounces. Represent the given situation as an equation.

Model the equation and find how much weight that puppy gained.

Solution :

Write a word equation based on the situation.

Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.

Let x represent the number of ounces gained.

Then, we have

Therefore, the equation 6 + x = 14 represents the given situation.

Let us model the equation 6 + x = 14 using algebra tiles.

To find how much weight that puppy gained, we have to solve for x.

To solve for x in the above model, we have to isolate x.

That is, we have to remove six 1 tiles on the left side.

Whenever we remove tiles from one side of the mat, we must remove the same number of tiles from the other side of the mat.

Cross out six 1 tiles on the left side and do the same on the other side.

In the above model, we find x on the left side and eight "1" tiles on the right side.

So, the value of x is 8.

Hence, the puppy gained 8 ounces of weight.

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