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Solving Inequalities

To solve an inequality you must get x alone on one side of the inequality symbol with a constant on
the other side of the symbol. To get x alone in an inequality you use the same steps as you used in
solving equations but there is one added condition . If you ever multiply or divide both sides of
the inequality by a negative number you must switch the direction of the inequality symbol.

Solve a one step inequality by getting
the variable x alone on one side of the inequality sign

Eliminate the constant term on the x side or eliminate the coefficient with the x term.
1. Eliminate the constant term on the x side of the equation by adding or subtracting the constant from
both sides of the inequality.
2. Eliminate the coefficient by multiplying or dividing both sides of the inequality by the coefficient. If
you ever multiply or divide both sides of the inequality by a negative number then you
must
switch the direction of the inequality symbol.

Examples of solving a one step inequality:

Example 1 Example 2 Example 3
add +6 to both sides divide both sides by –2
(switch the symbol)
multiply both sides by –4
(switch the symbol)
Example 4 Example 5 Example 6
subtract 5 from both sides divide both sides by 4 multiply both sides by 3

Solving Inequalities
Solve an inequality by getting the variable x
alone on one side of the inequality sign

Get the variable x alone using the same steps as you did in solving equations in Chapter 6.

1. Distribute and combine like terms on each side of the equal sign.

2. Get the x term on only one side of the equation by adding or subtracting the smallest x term from
both sides of the inequality.

3. Eliminate the constant term on the x side of the equation by adding or subtracting that constant from
both sides of the inequality.

5. Eliminate the coefficient by multiplying or dividing both sides of the inequality by the coefficient. If
you ever multiply or divide both sides of the inequality by a negative number then you
must switch the direction of the inequality symbol.

Example 1 Example 2 Example 3 Example 4
Example 5 Example 6 Example 7 Example 8
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