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MATH 101A / AD1-6


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Examples

1. 4(2x + 1) – 29 = 3(2x – 5)

8x + 4 – 29 = 6x – 15 Remove parentheses, using distributive property

 

8x – 25 = 6x – 15 Combine like terms

 

8x – 25 – 6x = 6x – 15 – 6x Subtract 6x from both sides; this will isolate variable terms

 

2x – 25 = -15 Combine like terms

 

2x – 25 + 25 = -15 + 25 Add 25 to both sides; this will isolateconstant terms

2x = 10

2x/2 = 10/2 Divide both sides by 2 to isolate the

variable

x = 5

2. [m/2 - 1/m] = 12m [(6m +5)/12] When the equation contains fractions, multiply

both sides by the LCD, 12m

12m/1 * m/2 – 12m/1 * 1/m = 12m/1 * (6m+5)/12

6m - 12 = m(6m + 5)

6m - 12 = 6m + 5m

6m - 12 - 6m = 6m + 5m - 6m

-12 = 5m

-12/g = 5m/5

-12/5 = m

 

3. three more than twice a certain number.

            = 2x + 3

 

 

4. The sum of two numbers is 50.

            X + y = 50

 

 

5. The square of the sum of 2x and y.

            (2x + y)^2

 

 

6. The square of the product of 5x and 2x

            ((5x)(2x))^2

          

 

7. Jeff is 7 yrs older than Tom who is half as old as Tracy. Express each of their ages in terms of a single unknown.

          Let x = Tracy

  x/2 = Tom

          x/2 + 7 = Jeff

 

 

8. Dan has 4 times as many $20 bills than $50 bills

            let x = $50

            4x = $20

 

 

9. The perimeter of the rectangle if one side is 4 more than the other side.

            2x + 2(x + 4)

 

 

10. John’s age 8 years ago if he is 12 years older than Carlo.

            X = age of Carlo     

X + 12 = present age of John

(x +12) – 8 = John’s age 8 years ago

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