Question

Ken is solving the inequality, 5 − 2x > 3, and has solved for x. His work is below. Choose the statement that is true regarding Ken's work.

A) The solution is incorrect. Ken should have added 2x on both sides.
B) The solution is incorrect. Ken should have added 5 instead of subtracting 5.
C) The solution is incorrect. Ken should have reversed the direction of the inequality sign.
D) Ken's work and solution is correct.

Answer 1

Ken should subtract 5 from both sides and then divide by -2, reversing the inequality sign, to properly solve the inequality. His work would be incorrect if he did not reverse the sign after dividing by a negative number.

Step-by-step explanation:

To determine the correctness of Ken's solution to the inequality 5 - 2x > 3, we must follow the appropriate steps to solve for x. Initially, we manipulate the inequality to isolate the variable on one side:

• Subtract 5 from both sides: -2x > -2.
• Divide both sides by -2, remembering that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign: x < 1.

Ken's solution should reflect these steps. Reversing the inequality sign is crucial when dealing with the multiplication or division of a negative number. Therefore, if Ken has not reversed the inequality sign after dividing by -2, his solution would be incorrect, aligning with statement C). However, without Ken's actual solution provided, we cannot affirm the correctness without seeing what he did after subtracting 5 from both sides.