Solving One-Step Inequalities by Multiplying or Dividing – Practice Problems

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For simple inequalities such as x < 5, we know all the values less than 5 are in the solution set. But, what if there is a coefficient to the variable such as with this inequality: 2x > 10. This is a one-step inequality problem, and we can solve this type of inequality problem by using the inverse of multiplication or division.

If a coefficient is multiplied with the variable, isolate the variable by dividing by the coefficient on both sides of the equation. If the coefficient divides the variable, isolate the unknown value by multiplying by the coefficient on both sides of the equation. Always, keep the inequality balanced. Whatever you do to one side of the sign you must do to the other side. Unlike solving one-step inequalities by addition and subtraction, for multiplication and division problems, you must also consider the direction of the inequality sign.

Remember the rule, if multiplying or dividing by a positive number, maintain the direction of the sign. When multiplying or dividing by a negative number, flip the sign over, so it points in the opposite direction.

It’s a good idea to check you work, to catch any careless errors you might make such as forgetting to flip the inequality sign. When graphing on the number line, an open dot is for greater than (>) and less than (

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Exercises in this Practice Problem
Explain the rules of the cavemen's game.
Calculate the number of times at least the first cavemen hit the bullseye.
Analyze the scores of the cavemen's friends.
Decide which sign has to be flipped to solve the inequality.
Define the meaning of each inequality sign.
Calculate the inequality $-2x-2 \ge (-2x+1) \times 4$.