# Workbook 1 - Solving Linear Equations

```Due: ___________________
Corrections Needed:
Name: ___________________________
Math 70: Solving Linear Equations
Where to look in your ALEKS pie: In the “Real Numbers and Linear Equations” slice, look at objectives relating to
“Solving a two-step equation”, “Solving a linear equation with several occurrences of the variable: Variables on
both sides and two distributions ”, and “Solving a ___ word problem …”.
Directions: For Exercises 1-8, solve each equation. Box or circle your final solution. If your solution is a fraction,
reduce it to lowest terms.
Exercise 1:
7
13 7
5
w  w
9
6 2
9
Exercise 2:
1
 y  3  3  y  5   2 y
5
10
5
Exercise 3:
0.0625  0.27 x  0.34  x
Exercise 4:
0.5  t  6  10.4  0.41  t 
Exercise 5:
9x  12  3x  2  x  8  5x
Exercise 6:
5 x  3 25 5  2 x


4
12
3
Exercise 7: 5  72  3x  5  x  4x  9




Exercise 8:  2 xx  3  3x 2  1  8  5 x 2  1
Directions:
For Exercises 9-10, answer each question by setting up and solving a linear equation. Make sure to
define your variable (i.e., say what x stands for) and answer each question with a complete sentence.
Exercise 9:
The product of three and the sum of a number and two-fifths is four-fifths less than negative two
times the number.
Exercise 10:
The quotient of three less than a number and three is the same as the quotient of one less than the
number and four.
Exercise 11:
In Astoria, a Penske ® 26-foot moving truck rental costs \$49.95 plus \$0.59 per mile for 6 hours. The
same truck from U-Haul ® costs \$39.95 and \$0.99 per mile for 6 hours.
(a.) Write the expression for the total cost of using the Penske truck.
(b.) Write the expression for the total cost of using the U-Haul truck.
(c.) How many miles need to be driven so that the amount of the Penske truck and the U-Haul truck are the
same?
```
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