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What is the solution to the equation?

[tex] \sqrt[3]{2x + 5} = 5 [/tex]

A. 240
B. 65
C. 60
D. 5

Sagot :

GinnyAnswer
To solve the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex], we will proceed step-by-step as follows:

1. Cubing Both Sides:
To eliminate the cube root, cube both sides of the equation:
[tex]\[ (\sqrt[3]{2x + 5})^3 = 5^3 \][/tex]
This simplifies to:
[tex]\[ 2x + 5 = 125 \][/tex]

2. Isolate [tex]\(2x\)[/tex]:
Subtract 5 from both sides to isolate [tex]\(2x\)[/tex]:
[tex]\[ 2x + 5 - 5 = 125 - 5 \][/tex]
[tex]\[ 2x = 120 \][/tex]

3. Solve for [tex]\(x\)[/tex]:
Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{120}{2} \][/tex]
[tex]\[ x = 60 \][/tex]

The correct solution to the equation [tex]\(\sqrt[3]{2x + 5} = 5\)[/tex] is [tex]\(x = 60\)[/tex].

Therefore, the correct answer is:
C. 60
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