Solving Linear Equations
Name
Solve the following equations.
1. 10  18  2x
a.
b.
c.
d.
x = -14
x = -4
x=4
x=6
2. 3x  4  8  x
a.
b.
c.
d.
x= 2
x=3
x=4
x=6
3. 6x  1  3x  2  2
a. x = -9
14
b. x 
3
c. All Real #’s
d. No Solution
Solve and check. Show all algebraic steps.
4. x  3  15
5. 3x  6  24
6. Is x = 4 a solution of 2x  5  12 ? Explain your answer using complete sentences.
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
1
Use the scenario below for questions #7-9.
Lisa Carr figures that it costs her 52 cents per mile to drive her car, plus a fixed monthly
cost of $335 for car payment and insurance.
7. Write a linear equation expressing her total monthly cost in terms of the number of
miles driven that month.
8. How much will it cost Lisa to drive 1000 miles a month?
9. Lisa can afford no more than $750 a month, total. How far can she drive each
month?
10. Write a linear equation which has no solution and show the algebraic steps to
support your answer.
11. Pat and Nancy each solved the following equation: 3x  5  17
Pat’s Work
Nancy’s Work
3x  5  17
3 x  5  17
3 x  22
x  66
3x  12
x4
a. Who has the correct answer and how did you decide?
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
2
Improving Student Achievement in Algebra, Grades 7-12. The DuPage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
3