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: Solving linear inequalities and equations are not identical because multiplying/dividing by a negative reverses the inequality sign (not done in equations), so A is incorrect.
• Option B: Replacing the inequality symbol with an equal sign changes the solution set (inequalities have ranges, equations have specific solutions), so B is incorrect.
• Option C: The steps (like isolating the variable) are mostly the same, except when multiplying/dividing by a negative (which reverses the inequality sign, not applicable to equations), so C is correct.

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.