Solve the Rational Equation for x square root of 3x-2=6

$\sqrt{3 x - 2} = 6$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{3 x - 2}}^{2} = 6^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 2}$ as ${(3 x - 2)}^{\frac{1}{2}}$ .

${({(3 x - 2)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(3 x - 2)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 2)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(3 x - 2)}^{1} = 6^{2}$

Simplify.

$3 x - 2 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$3 x - 2 = 36$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$3 x = 36 + 2$

Add $36$ and $2$ .

$3 x = 38$

Divide each term in $3 x = 38$ by $3$ and simplify.

Divide each term in $3 x = 38$ by $3$ .

$\frac{3 x}{3} = \frac{38}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{38}{3}$

Divide $x$ by $1$ .

$x = \frac{38}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{38}{3}$

Decimal Form:

$x = 12.\overline{6}$

Mixed Number Form:

$x = 12 \frac{2}{3}$

Solve the Rational Equation for x square root of 3x-2=6

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