Question

Which of the following represents the correct solutions to the inequalities 2x - 3 < 11, 3x + 59 < 12, and √2x + 3 > 5, respectively?

a. x < 7, x < -15, x > 5 - √2
b. x > 7, x > -15, x < 5 - √2
c. x < 7, x > -15, x > 5 - √2
d. x > 7, x < -15, x < 5 - √2

Answer 1

After solving each inequality separately, we found the correct solutions to be x < 7, x < -15, and x > 2. None of the provided options correctly represent the solution for the third inequality.

Step-by-step explanation:

To find the correct solutions to the inequalities 2x - 3 < 11, 3x + 59 < 12, and √2x + 3 > 5, we need to solve each separately.

• For the first inequality, 2x - 3 < 11, add 3 to both sides to get 2x < 14 and then divide both sides by 2 to find x < 7.
• For the second inequality, 3x + 59 < 12, subtract 59 from both sides to get 3x < -47 and then divide by 3 to find x < -15.67, which rounds to x < -15.
• For the third inequality, √2x + 3 > 5, first subtract 3 from both sides to get √2x > 2, then square both sides to remove the square root, getting 2x > 4. Finally, divide by 2 to get x > 2.

So the correct solutions to the inequalities are x < 7, x < -15, and x > 2; therefore, the provided options do not include the correct solution for the third inequality.