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**6.1 Solving One-Step Inequalities**

Algebra 6.1 Solving One-Step Inequalities

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**Two Mistakes on This Slideshow**

See if you can spot them!

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x ≤ 4 The graph of an inequality is the set of points on a number line that are solutions. The graph is a boundary point and a line with an arrow pointing left or right.

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x > 2 A hollow point means that the number is not included in the set of solutions. Use a hollow point to graph < and > inequalities.

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x ≥ -3 A solid point means that the number is included in the set of solutions. Use a solid point to graph ≤ and ≥ inequalities.

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**< x -1 The arrow points left for < and ≤ .**

x < -1 The arrow points left for < and ≤ . The arrow points right for > and ≥ . The direction of the arrow tip is the same as the direction of the inequality symbol when the variable is on the left side.

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**Solve inequalities just as you would linear equations in one variable**

Solve inequalities just as you would linear equations in one variable. Isolate the variable. Then graph the solution. x - 5 > -4 x > 1 -1 1 2 3 4 15a ≤ -60 -7 -6 -5 -4 -3 -2 a ≤ -4

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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) Multiply by positive 20 > 10 Inequality stays true 20 > 10 (-2) (-2) Multiply by negative -40 > -20 Inequality not true < Reverse direction of inequality symbol -40 -20

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**≤ 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 Reverse direction of inequality symbol ≤ a -8

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**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

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**Solve the following inequalities and graph each solution**

Solve the following inequalities and graph each solution. Write the variable on the left in your solution. 42 > x x < 42 39 40 41 42 43 44 -3 < x x > -3 2 > -1 - x -5 -4 -3 -2 -1

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Homework Pg #31 – 61 odd,

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