**Using subtraction to solve equations :**

Addition and subtraction equations are the equations which contain addition or subtraction.

For example,

x + 5 = 7

y - 3 = 4

We use subtraction to solve equations which contain addition.

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

**Example 1 :**

Solve the equation a + 15 = 26. 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.

aaaaaaaaaaaaaaaaaaaaaaaa + 15 = 26 aaaaaaaaaaaaaaaaaaaaaaaa- 15aa- 15 aaaaaaaaaaaaaaaaaaaaaa-------------- aaaaaaaaaaaaaaaaaaaaaaaa = 11 aaaaaaaaaaaaaaaaaaaaaa--------------

Hence, the value of "a" is 11.

Graphing the solution on a number line.

**Example 2 :**

Solve the equation 5 = w + 1.5. Graph the solution on a number line.

**Solution :**

5 = w + 1.5

Since we are trying to solve for "w", we have to get rid of 1.5 which is added to "w".

To get rid of 1.5, we have to subtract 1.5 on both sides.

(5) - 1.5 = (w + 1.5) - 1.5

3.5 = w

Hence, the value of "w" is 3.5.

Graphing the solution on a number line.

**Example 3 :**

Solve for x : x + 7 = 8

**Solution :**

x + 7 = 8

Since we are trying to solve for "x", we have to get rid of 7 which is added to "x".

To get rid of 7, we have to subtract 7 on both sides.

aaaaaaaaaaaaaaaaaaaaaaax + 7 = 8 aaaaaaaaaaaaaaaaaaaaaaaaa- 7aa- 7 aaaaaaaaaaaaaaaaaaaaaa------------- aaaaaaaaaaaaaaaaaaaaaaax = 1 aaaaaaaaaaaaaaaaaaaaaa-------------

Hence, the value of "x" is 1.

**Example 4 :**

Solve for a : a + 3 = 11

**Solution :**

a + 3 = 11

Since we are trying to solve for "a", we have to get rid of 3 which is added to "a".

To get rid of 3, we have to subtract 3 on both sides.

aaaaaaaaaaaaaaaaaaaaaaaa + 3 = 11 8 aaaaaaaaaaaaaaaaaaaaa a- 3aa- 3 7 aaaaaaaaaaaaaaaaaaaaa------------- aaaaaaaaaaaaaaaaaaaaa a = 8 aaaaaaaaaaaaaaaaaaaaaa-------------

Hence, the value of "a" is 8.

**Example 5 :**

When 7 is added to a number, we get 25. Find the number.

**Solution : **

Let "x' be the required number.

According to the question, we have

x + 7 = 25

Here "7" is added to "x". To get rid of 7, we have to subtract 7 on both sides and solve the equation as explained below.

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

x = 18

Hence, the required number is "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.

According to the question, we have

x + 7.5 = 22.5

Here "7.5" is added to "x". To get rid of 7.5, we have to subtract 7.5 on both sides and solve the equation as explained below.

(x + 7.5) - 7.5 = 22.5 - 7.5

x = 15

Hence, the other number is 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.

After having gone through the stuff given above, we hope that the students would have understood "Using subtraction to solve equations".

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