Solve for w square root of 3-2/3w+8=11

$\sqrt{3 - \frac{2}{3} w} + 8 = 11$

Step 1

Move all terms not containing $\sqrt{3 - \frac{2}{3} w}$ to the right side of the equation.

Subtract $8$ from both sides of the equation.

$\sqrt{3 - \frac{2}{3} w} = 11 - 8$

Subtract $8$ from $11$ .

$\sqrt{3 - \frac{2}{3} w} = 3$

Step 2

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

${\sqrt{3 - \frac{2}{3} w}}^{2} = 3^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify each term.

Combine $w$ and $\frac{2}{3}$ .

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

Move $2$ to the left of $w$ .

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

Simplify.

$3 - \frac{2 w}{3} = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$3 - \frac{2 w}{3} = 9$

Step 4

Solve for $w$ .

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

Subtract $3$ from both sides of the equation.

$- \frac{2 w}{3} = 9 - 3$

Subtract $3$ from $9$ .

$- \frac{2 w}{3} = 6$

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 w}{3}) = - \frac{3}{2} \cdot 6$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{2} (- \frac{2 w}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 w}{3}) = - \frac{3}{2} \cdot 6$

Move the leading negative in $- \frac{2 w}{3}$ into the numerator.

$\frac{- 3}{2} \cdot \frac{- 2 w}{3} = - \frac{3}{2} \cdot 6$

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 w}{3} = - \frac{3}{2} \cdot 6$

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 w$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - w = - \frac{3}{2} \cdot 6$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 w = - \frac{3}{2} \cdot 6$

Multiply $w$ by $1$ .

$w = - \frac{3}{2} \cdot 6$

Simplify the right side.

Simplify $- \frac{3}{2} \cdot 6$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$w = \frac{- 3}{2} \cdot 6$

Factor $2$ out of $6$ .

$w = \frac{- 3}{2} \cdot (2 (3))$

Cancel the common factor.

$w = \frac{- 3}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$w = - 3 \cdot 3$

Multiply $- 3$ by $3$ .

$w = - 9$

Solve for w square root of 3-2/3w+8=11

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