Question

explain how solving a linear inequality is similar to solving a linear equation.

choose the correct answer below.

a. the steps for solving a linear inequality are identical to the steps for solving a linear equation.

b. if the inequality symbol is replaced by the equal sign, the solution set does not change.

c. the steps for solving a linear inequality are identical to the steps for solving a linear equation except when multiplication or division by a negative number happens.

Explanation:

To determine the correct answer, we analyze each option:

• Option A: The steps are not identical because multiplying/dividing by a negative reverses the inequality sign, which isn't done in linear equations. So A is incorrect.
• Option B: Replacing the inequality symbol with an equal sign changes the solution set (inequality has a range, equation has a single solution or set, and sign reversal can affect it). So B is incorrect.
• Option C: For linear inequalities and equations, most steps (like adding/subtracting, simplifying) are the same. The key difference is when multiplying or dividing by a negative number, the inequality sign reverses, which doesn't happen in linear equations. So C correctly describes the similarity (most steps same) with the noted exception.

Answer:

C. The steps for solving a linear inequality are identical to the steps for solving a linear equation except when multiplication or division by a negative number happens.