AlgebraAlgebra

6.1 6.1

Solving One-Step InequalitiesSolving One-Step Inequalities

Two Mistakes on This Two Mistakes on This SlideshowSlideshow

See if you can spot them!See if you can spot them!

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

The graph of an inequality is the set of The graph of an inequality is the set of points on a number line that are points on a number line that are solutions.solutions.

The graph is a boundary point and a line The graph is a boundary point and a line with an arrow pointing left or right.with an arrow pointing left or right.

x ≤ 4

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

A hollow point means that the A hollow point means that the number is number is notnot included in the set included in the set of solutions. of solutions.

Use a hollow point to graph < Use a hollow point to graph < and > inequalities.and > inequalities.

x > 2

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

x ≥ -3

A solid point means that the number A solid point means that the number isis included in the set of solutions. included in the set of solutions.

Use a solid point to graph ≤ and ≥ Use a solid point to graph ≤ and ≥ inequalities.inequalities.

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

x

The arrow points left for < and ≤ . The arrow points left for < and ≤ . The arrow points right for >The arrow points right for > and ≥ .and ≥ .

The direction of the arrow tip is the The direction of the arrow tip is the same as the direction of the inequality same as the direction of the inequality symbol when the variable is on the left symbol when the variable is on the left side.side.

< -1

Solve inequalities just as you would linear equations in one variable. Isolate the variable. Then graph the solution.

x - 5 > -4

x > 1 -1 0 1 2 3 4

15a ≤ -60

a ≤ -4

-7 -6 -5 -4 -3 -2

+ 5 +5

15 15

The only difference between solving an inequality and an equation is what happens when both sides are multiplied or divided by a negative value.

10 > 5

(2) (2)

20 > 10 Inequality stays true

Multiply by positive

20 > 10(-2) (-2) Multiply by negative

-40 > -20 Inequality not true

-40 < -20 Reverse direction of inequality symbol

When solving an inequality, REVERSE THE DIRECTION OF THE INEQUALITY SYMBOL if you multiply or divide by a negative value.

-¾a ≥ 6 Multiply by -4/3

a ≤ -8Reverse direction of inequality symbol

4

3

4

3

Solve the following inequalities and graph each solution.

¼x > -8 x > -32

-34 -33 -32 -31 -30 -29

a ≤ 50

47 48 49 50 51 52

510

a

Solve the following inequalities and graph each solution. Write the variable on the left in your solution.

x < 42

39 40 41 42 43 44

-3 < x

-5 -4 -3 -2 -1 0

67

x

42 > x

2 > -1 - xx > -3

HomeworkHomework

Pg. 337 #31 – 61 odd, 71-87Pg. 337 #31 – 61 odd, 71-87