# USING ADDITION TO SOLVE EQUATIONS

## About "Using addition to solve equations"

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.

## Using addition to solve equations - Examples

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 1/4.

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".

Apart from the stuff given above, if you want to know more about "Using addition to solve equations", please click here

Apart from "Using addition to solve equations", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6