1

Problem

Solve the inequality \$\sqrt (2x + 3) - 4 > 0\$.

2

Step

The given

\$\sqrt (2x + 3) - 4 > 0\$

3

Step

Add 4 to both sides of the inequality to isolate the square root term and then simplify:

\$\sqrt (2x + 3) - \cancel4 + \cancel4 > 0 + 4\$

\$\sqrt (2x + 3) > 4\$

4

Step

Squaring on both sides of the inequality to eliminate the square root:

\$\sqrt (2x + 3)^2 > 4^2 \$

2x + 3 > 16

5

Step

Subtract 3 from both sides and divide both sides by 2:

\$2x + \cancel3 - \cancel3 > 16 - 3 \$

2x > 13

\$ x > (13)/2 \$

6

Solution

Therefore, the solution to the inequality is \$ x > (13)/2 \$.

7

Sumup

Please summarize steps

Choices

8

Choice-A

This option suggests that x is greater than a negative value, which contradicts the solution \$ x > (13)/2 \$

Wrong \$ x > -(13)/2 \$

9

Choice-B

This option suggests that x is less than \$(13)/2\$, which is the opposite of the solution \$ x > (13)/2 \$

Wrong \$ x < (13)/2 \$

10

Choice-C

This option correctly represents the solution, indicating that x is greater than \$ (13)/2 \$

Correct \$ x > 13/2 \$

11

Choice-D

This option suggests that x is less than a negative value, which contradicts the solution \$ x > (13)/2 \$

Wrong \$ x < -(13)/2 \$

12

Answer

Option

C

13

Sumup

Please summarize choices