**
**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