Problem Solving with Simple Inequalities

Solving Inequalities

How can you solve an inequality?

How can you solve an inequality?

• An inequality uses <, >, ≤, ≥, and ≠ to compare two expressions.

• Inequalities have an infinite number of solutions.

• EXAMPLE: x > 5

• One solution is to use x = 7 because 7 > 5.

Graph all of the solutions of x > 5.

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To graph x > 5, draw an open circle at 5 on a number line.

• It is an open circle because <, > get open circles.

• ≤, ≥ get closed circles.

Find several solutions and color those on a number line.

7 and 9 are solutions because 7 > 5 and 9 > 5.

Start at the open circle and color over the solutions you found. Draw an arrow to show that the solutions go on forever.

Graphing Inequalities

Now it is your turn!

Remember to use a graph check your inequalities.

Open Ended

Name three solutions for y < 3.

Open Ended

Name three solutions for c ≥ 5.

Open Ended

Name three solutions for m > 22.

Open Ended

Name three solutions for z ≤ 11.

Open Ended

Name three solutions for h > 8.

Poll

How do you feel about solving inequalities?

• Great!

• So-So.

• Confused?

Hotspot

The graph of $$3x-y=1$$ is shown on the grid.

Which points are in the solution set of $$3x-y\ge1$$ ?

Select THREE correct circles that represent the points.