**Using addition 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 addition to solve equations which contain subtraction.

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

**Example 1 :**

Solve the equation y - 21 = 18. Graph the solution on a number line.

**Solution :**

y - 21 = 18

Since we are trying to solve for "y", we have to get rid of 21 which is subtracted from "y".

To get rid of 21, we have to add 21 on both sides.

aaaaaaaaaaaaaaaaaaaaaaay - 21 = 18 aaaaaaaaaaaaaaaaaaaaaaaa + 21aa +21 aaaaaaaaaaaaaaaaaaaaaa-------------- aaaaaaaaaaaaaaaaaaaaaaay = 39 aaaaaaaaaaaaaaaaaaaaaa--------------

Hence, the value of "y" is 39.

Graphing the solution on a number line

**Example 2 :**

Solve the equation h - 1/2 = 3/4. Graph the solution on a number line.

**Solution :**

h - 1/2 = 3/4

Since we are trying to solve for "h", we have to get rid of 1/2 which is subtracted from "h".

To get rid of 1/2, we have to add 1/2 on both sides.

(h - 1/2) + 1/2 = (3/4) + 1/2

h = 3/4 + 2/4

h = 5/4

h = 1 1/4

Hence, the value of "h" is 1 1/4.

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 subtracted from "x".

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

aaaaaaaaaaaaaaaaaaaaaaax - 7 = 8 aaaaaaaaaaaaaaaaaaaaaaaaa+ 7aa+ 7 aaaaaaaaaaaaaaaaaaaaaa------------- aaaaaaaaaaaaaaaaaaaaaaax = 15 aaaaaaaaaaaaaaaaaaaaaa-------------

Hence, the value of "x" is 15.

**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 subtracted from "a".

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

aaaaaaaaaaaaaaaaaaaaaaaa - 3 = 11 8 aaaaaaaaaaaaaaaaaaaaa a+ 3aa+ 3 7 aaaaaaaaaaaaaaaaaaaaa------------- aaaaaaaaaaaaaaaaaaaaa a = 14 aaaaaaaaaaaa aaaaaaaa-------------

Hence, the value of "a" is 14.

**Example 5 :**

When 7 is subtracted from a number, we get 15. Find the number.

**Solution : **

Let "x' be the required number.

According to the question, we have

x - 7 = 15

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

(x - 7) + 7 = (15) + 7

x = 22

Hence, the required number is "22".

**Example 6 :**

The difference between the two numbers is 22.5. If the smaller number is 7.5, find the larger number

**Solution : **

Let "x' be the larger number.

According to the question, we have

x - 7.5 = 22.5

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

(x - 7.5) + 7.5 = 22.5 + 7.5

x = 30

Hence, the larger number is 30.

**Example 7 :**

Sarah used a gift card to buy $3 worth of food. She has $2 left on her gift card. Write an equation to represent this situation.

Model the equation and find how much money that she had initially in her gift card.

**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 be the amount on the card.

Then, we have

Therefore, the equation "x - 3 = 2" represents the given situation.

Let us model the equation "x - 3 = 2" using algebra tiles.

To find how much money that Sarah had initially, 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 "-1" tiles from one side of the mat, we must add the same number of "1" tiles on both sides.

Cross out one "-1" tile for one "1" tile.

Then, we have

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

So, the value of "x" is 5.

Hence, Sarah had $5 initially in her gift card.

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

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