USING SUBTRACTION TO SOLVE EQUATIONS

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.

Example 8 :

The altitude a (in feet) of a plane t minutes after liftoff is given by a = 3400t + 600. How many minutes after liftoff is the plane at an altitude of 21,000 feet?

Solution :

Here a = altitude and t = number of minutes after lift off

a = 3400t + 600

21000 = 3400t + 600

3400 t = 21000 - 600

3400t = 20400

t = 20400/3400

t = 6

So, 6 minutes after the lift off the plane will be at altitude of 21000 ft.

Example 9 :

A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car.

Solution :

Let x be the number of hours.

Repair bill = 553

Cost of parts = 265

Labour cost = $48

48x + 265 = 553

48x = 553 - 265

48x = 288

x = 288/48

x = 6

So, the number of hours of labour is 6.

In the following problems write and solve an equation to find the number.

Example 10 :

The sum of twice a number and 13 is 75.

Solution :

Let x be the number, then twice the number be 2x

Sum of the numbers = 75

2x + 13 = 75

2x = 75 - 13

2x = 62

x = 62/2

x = 31

So, the required number is 31.

Example 11 :

The difference of three times a number and 4 is −19.

Solution :

Let x be the required number

3x be three times a number.

The difference of numbers = -19

3x - 4 = -19

3x = -19 + 4

3x = -15

x = -15/3

x = -5

3x = 3(-5) ==> -15

So, the required numbers are -15 and 4.

Example 12 :

Eight plus the quotient of a number and 3 is −2.

Solution :

Let x be the required number.

8 + (x/3) = -2

x/3 = -2 - 8

x/3 = -10

x = -10(3)

x = -30

So,. the required number is -30.

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