WHICH VALUE OF X SATISFIES THE EQUATION

Find the value of x which satisfies the given equation :

Example 1 :

x + 11 = 17

Solution :

x + 11 = 17

Subtract 11 from both sides.

x = 6

Example 2 :

3x + 4  =  25

Solution :

3x + 4  =  25

Subtract 4 from both sides.

3x = 21

Divide both sides by 3.

x = 7

Example 3 :

5x + 3 = 17 - 2x

Solution :

5x + 3 = 17 - 2x

Add 2x to both sides.

7x + 3 = 17

Subtract 3 from both sides.

7x = 14

Divide both sides by 7.

x = 2

Example 4 :

12 - x = 8

Solution :

12 - x = 8

Subtract 12 from both sides.

-x = -4

Multiply both sides by -1.

x = 4

Example 5 :

x/6 = 7

Solution :

x/6 = 7

Multiply both sides by 6.

x = 42

Example 6 :

(3x + 2)/4 = 5

Solution :

(3x + 2)/4 = 5

Multiply both sides by 4.

3x + 2 = 20

Subtract 2 from both sides.

3x = 18

Divide both sides by 3.

x = 6

Example 7 :

2x/3 + 1/2 = 5/6

Solution :

2x/3 + 1/2 = 5/6

The least common multiple of the denominators (3, 2, 6) is 6.

Multiply both sides by 6 to get rid of the denominators.

6(2x/3 + 1/2) = 6(5/6)

Using distributive property,

6(2x/3) + 6(1/2)  =  5

2(2x) + 3  =  5

4x + 3 = 5

Subtract 3 from both sides.

4x = 2

Divide both sides by 4.

x = 1/2

Example 8 :

2x/3 + x/6 = 5

Solution :

2x/3 + x/6 = 5

The least common multiple of the denominators (3, 6) is 6.

Multiply both sides by 6 to get rid of the denominators.

6(2x/3 + x/6) = 6(5)

Using distributive property,

6(2x/3) + 6(x/6) = 30

2(2x) + x = 30

4x + x = 30

5x = 30

Divide both sides by 5.

x = 6

Example 9 :

(x - 2)/3 + 1/6 = 5/6

Solution :

(x − 2)/3 + 1/6 = 5/6 

The least common multiple of the denominators (3, 6) is 6.

Multiply both sides by 6 to get rid of the denominators.

6[(x − 2)/3 + 1/6] = 6(5/6)

Using distributive property,

6[(x - 2)/3] + 6(1/6) = 5

2(x - 2) + 1 = 5

2x - 4 + 1 = 5

2x - 3 = 5

Add 3 to both sides.

2x = 8

Divide both sides by 2.

x = 4

Example 10 :

The number of people on the school board is represented by x. Two subcommittees with an equal number of members are formed, one with (2x/3) - 5 members and the other with x/4 members. How many people are on the school board? 

Solution :

From the given information, it is clear that we have to find the value of x which satisfies the following equation.

2x/3 - 5 = x/4

(2x - 15)/3 = x/4

The least common multiple of the denominators (3, 4) is 12.

Multiply both sides by 12 to get rid of the denominators.

12[(2x - 15)/3] = 12(x/4)

4(2x - 15) = 3x

8x - 60 = 3x

Subtract 3x from both sides.

8x - 60 = 3x

5x - 60 = 0

Add 60 to both sides.

5x = 60

Divide both sides by 5.

x = 12

There are 12 people on the school board. 

Example 11 :

Use the values −2, 5, 9, and 10 to complete each statement about the equation ax = b − 5.

a) When a = ___ and b = ___, x is a positive integer.

b) When a = ___ and b = ___, x is a negative integer.

Solution :

a)  ax = b − 5

When a = 5 and b = 10

5x = 10 - 5

5x = 5

x = 1

1 is a positive integer.

b)

When a = -2 and b = 9

-2x = 9 - 5

-2x = 4

x = 4/(-2)

x = -2

-2 is a negative integer.

Example 12 :

The circle graph shows the percents of different animals sold at a local pet store in 1 year.

a) What percent is represented by the entire circle?

b) How does the equation 7 + 9 + 5 + 48 + x = 100 relate to the circle graph? How can you use this equation to find the percent of cats sold?

Solution :

a) The entire circle will represents 100%.

b) Percentages of

dog + cat + bird + rabbit + hamster = 100

5 + 9 + 7 + x + 48 = 100

69 + x = 100

x = 100 - 69

x = 31

Example 13 :

Describe and correct the error in solving the equation.

Solution :

Given that, 

-0.8 + r = 12.6

To solve for r, we have to add 0.8 on both sides

-0.8 + 0.8 + r = 12.6 + 0.8

r = 13.4

The error is 

Instead of adding 0.8, they are subtracting 0.8.

Solution :

Given that, 

-m/3 = -4

To solve for m, we have to multiply by 3 on both sides

-m = -4(3)

-m = -12

Dividing by -1 on both sides, we get

m = 12

The error is 

Cancelling the negative on both sides, we get 12.

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