Solving Multi-Step Inequalities – Practice Problems

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Just like equations, inequality problems can require multiple steps to calculate the answer. The steps to solve multi-step inequality problems start out the same as the steps to solve multi-step equations.

First, if parentheses are used in the problem, simplify those terms. Use the Distributive Property if needed. Next step, collect the like terms by adding and subtracting. After that, solve for the variable using opposite operations. This all seems the same – but watch out. The difference is the inequality sign. Your last step in solving the problem is to attend to the inequality sign.

To solve for the variable, if you multiplied or divided by a negative number, you must flip the inequality sign, so it points in the opposite direction. In other words, if you multiply or divide by a negative number, greater than (>) becomes less than (

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Exercises in this Practice Problem
How to set up an inequality.
Determine the number of workout sessions Rocky needs to reach his goal of losing $20$ pounds.
Decide how many workout sessions Bruno needs to complete.
Examine the effect of different diets on the Rocky's weight loss.
Describe the steps required to solve the inequality $-5x+(2\times5)\le -20$.
Solve the given inequalities.