If \sqrt{4x + 9} = 5, what is the value of x? — SAT

If $\sqrt{4x + 9} = 5$ , what is the value of $x$ ?

Answer: 4

Squaring both sides of the equation

\sqrt{4x + 9} = 5

yields

4x + 9 = 25

. Subtracting 9 from both sides gives

4x = 16

, and dividing by 4 yields

x = 4

. Checking this solution in the original equation yields

\sqrt{4(4) + 9} = \sqrt{25} = 5

, which confirms it is correct.

Square both sides of the equation

4x + 9 = 25

To eliminate the square root on the left side of the equation.

Subtract 9 from both sides of the equation

4x = 16

To isolate the variable term on the left side of the equation.

Divide both sides of the equation by 4

x = 4

To solve for

x

Substitute the solved value back into the original equation

\sqrt{4(4) + 9} = 5 \implies 5 = 5

To ensure the solution is valid and not extraneous.

Solving radical equations of the form

\sqrt{ax + b} = c

by squaring both sides.

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