If \sqrt{3x - 2} = 4, what is the value of x? — ACT

If $\sqrt{3x - 2} = 4$ , what is the value of $x$ ?

Answer: 6

The value of

x

is 6.

Squaring both sides of the equation

\sqrt{3x - 2} = 4

eliminates the radical, leading to

3x - 2 = 16

. Adding 2 to both sides results in

3x = 18

. Dividing both sides by 3 gives

x = 6

. Substituting 6 back into the original equation yields

\sqrt{3(6) - 2} = \sqrt{18 - 2} = \sqrt{16} = 4

, which verifies that the solution is correct.

Square both sides of the equation to remove the radical.

3x - 2 = 16

Squaring a square root removes the radical sign since

(\sqrt{a})^2 = a

for non-negative values.

Add 2 to both sides of the equation.

3x = 18

Adding the constant term moves it to the other side to isolate the term containing the variable.

Divide both sides by 3.

x = 6

Dividing by the coefficient of

x

yields the final solution.

Solving basic radical equations by isolating the radical and squaring both sides.

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