Answer:
x = 27
Step-by-step explanation:
[tex] \sqrt{2x - 5} = 7 [/tex]
Square both sides.
[tex] (\sqrt{2x - 5})^2 = 7^2 [/tex]
[tex] 2x - 5 = 49 [/tex]
Add 5 to both sides.
[tex] 2x = 54 [/tex]
Divide both sides by 2.
[tex] x = 27 [/tex]
Since we squared both sides, we must check the solution.
[tex] \sqrt{2x - 5} = 7 [/tex]
[tex] x = 27 [/tex]
[tex] \sqrt{2 \times 27 - 5} = 7 [/tex]
[tex] \sqrt{54 - 5} = 7 [/tex]
[tex] \sqrt{49} = 7 [/tex]
[tex] 7 = 7 [/tex]
Since when replacing x with 27 in the original equation, we get 7 = 7, which is a true statement, the solution x = 27 is correct.
Answer: x = 27
