Linear Inequalities in one variable

Inequality with one variable to the first power.for example: 2x-3<8

A solution is a value of the variable that makes the inequality true.x could equal -3, 0, 1, etc

Linear Inequalities in one variable

Transformations for Inequalities

Add/subtract the same number on each side of an inequality (as with a linear equation)

Multiply/divide by the same positive number on each side of an inequality

If you multiply or divide by a negative number, you MUST flip the inequality sign!

Ex: Solve the inequality

2x-3<8 +3 +3

2x<112 2 x< 5.5

1373 x

63 x

2x

Flip the sign when dividing by the -3!

RecallGraphing a linear Equality with

one variable…..

x = 4

Notice the circle is closed

Graphing a linear Inequality with one variable…..

x < 4

Notice the circle is open

Graphing a linear Inequality with one variable…..

x > -2

Notice the circle is open

Graphing a linear Inequality with one variable…..

x < 4

Notice the circle is closed

Graphing a linear Inequality with one variable…..

x ≥ -2

Notice the circle is closed

Will the circle be closed or open?

1.) x = 62.) x > 03.) x < -34.) x > -15.) x < 7

• 1.) closed• 2.) open• 3.) open• 4.) closed• 5.) closed

Solving a linear Inequality

• p + 5 > 3• p + 5 - 5 > 3 - 5• p > -2

Solve the following linear equation and illustrate your answer graphically

Solving a linear Inequality

• 3x < 9• 3x / 3 < 9 / 3• x < 3

Solving a linear Inequality

• -x < 4• -x/ -1 < 4 / -1• x > -4

The sign flips when you multiply or divide by a negative

Solving a 3-step inequality

• 2x - 4 < 4x - 1• 2x -4x - 4 < 4x -4x - 1• -2x - 4 < - 1• -2x -4 + 4 < - 1+4• -2x < 3• -2x/-2 < 3/-2

2x – 4 < 4x – 1• x > -3/2

Solving a compound inequality

• To solve a compound inequality, apply the same rules as before – but apply them to both sides of the inequality:

-3 < 2x-1 ≤ 5 (add 1 to both sides of the inequality)-2 < 2x ≤6-1 < x ≤ 2 (divide through by 2)

-2 0 2