Solving Two-Step Inequalities – Practice Problems

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Just like equations, inequality problems can require two-steps to calculate the solution. To solve, just like a two-step equality, use the Distributive Property to eliminate any parentheses.

Now Step 1: use the opposite operations of addition or subtraction to isolate the variable from the constant.

Step 2: use the opposite operations of multiplication or addition to isolate the variable from the coefficient. Remember to keep the inequality balanced, whatever you do to one side of the inequality sign you must do to the other.

Now, different from equations, you must consider the direction of the sign. If you multiplied or divided by a positive number, maintain the sign but if you multiply or divide by a negative number, you must flip the sign over so it points in the opposite direction.

Plotting the inequality on a number line lets you see the all the possible solutions. Use common sense, is a negative value reasonable for the problem you are solving? If not, determine that the least possible solution is zero, and indicate this in your answer. Remember an open dot is used to represent solutions that are less than or greater than, and a closed dot is used for solutions that are greater than and equal to or less than and equal to.

Use inequalities to solve problems. CCSS.MATH.CONTENT.HSA.CED.A.3

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Exercises in this Practice Problem
Determine how Miss. Crazycat can estimate the number of cats.
Estimate the number of cats in Miss. Crazycat's apartment.
Write an inequality to describe a number line.
Describe how Miss. Crazydog can estimate the number of dogs living in her home.
Describe the meaning of the inequality sign $\le$.
Solve the following inequalities.