Algebra 1
Solving Inequalities
To solve an inequality, simply solve it just like an equation but with the inequality in the
place of the equal sign. When you are done, don’t forget to graph it!!
Solving an Equation:
Solving an inequality:
2 x  5  11
2 x  5  11
 5  5
 5  5
2 x 16

2
2
x8
2 x 16

2
2
x8
Solve the equation and then solve the inequality next to it. Don’t forget to graph your
final answer for the inequality.
1.
3x  7  5
2.
3x  7  5
3.
1
x7 9
2
4.
1
x7 9
2
5. 2( x  3)  4  7
6. 2( x  3)  4  7
If both sides of an inequality are multiplied or divided by a negative, the direction of
the inequality switches.
 2x  7  5
7 7
 2x  2

2
2
x 1
Each inequality below has a step where both sides of the inequality are multiplied or
divided by a negative. When this happens, switch the direction of the inequality and
graph the final answer.
7.  4x  5  13
9.
2
( x  5)  18
5
8. 5  3x  4
10.  5( x  2)  6  17