42 (option D)
Explanation:
[tex]\begin{gathered} \text{Given:} \\ -7\text{ + }\sqrt[]{2x\text{ - 3}}\text{ = 2} \end{gathered}[/tex]
Add 7 to both sides:
[tex]\begin{gathered} -7\text{ + 7 + }\sqrt[]{2x\text{ - 3}}\text{ = 2 +7} \\ 0\text{ + }\sqrt[]{2x\text{ - 3}}\text{ = 9} \\ \text{ }\sqrt[]{2x\text{ - 3}}\text{ = 9} \end{gathered}[/tex]
Square both sides:
[tex]\begin{gathered} \text{ (}\sqrt[]{2x\text{ - 3}}\text{ = 9} \\ (\text{ }\sqrt[]{2x\text{ - 3}})^2=9^2 \\ 2x\text{ - 3 = 81} \\ \text{Add 3 to both sides:} \\ 2x\text{ - 3 + 3 = 81 + 3} \end{gathered}[/tex][tex]\begin{gathered} 2x\text{ = 84} \\ \text{divide both sides }by\text{ 2:} \\ \frac{2x}{2}\text{ =84/2} \\ x\text{ = 42 (option D)} \end{gathered}[/tex]
