Solve for z 7- square root of 3z+2=4

$7 - \sqrt{3 z + 2} = 4$

Step 1

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

Subtract $7$ from both sides of the equation.

$- \sqrt{3 z + 2} = 4 - 7$

Subtract $7$ from $4$ .

$- \sqrt{3 z + 2} = - 3$

Step 2

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

${(- \sqrt{3 z + 2})}^{2} = {(- 3)}^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

Apply the product rule to $- {(3 z + 2)}^{\frac{1}{2}}$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply ${({(3 z + 2)}^{\frac{1}{2}})}^{2}$ by $1$ .

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(3 z + 2)}^{1} = {(- 3)}^{2}$

Simplify.

$3 z + 2 = {(- 3)}^{2}$

Simplify the right side.

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

$3 z + 2 = 9$

Step 4

Solve for $z$ .

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

Subtract $2$ from both sides of the equation.

$3 z = 9 - 2$

Subtract $2$ from $9$ .

$3 z = 7$

Divide each term in $3 z = 7$ by $3$ and simplify.

Divide each term in $3 z = 7$ by $3$ .

$\frac{3 z}{3} = \frac{7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 z}{3} = \frac{7}{3}$

Divide $z$ by $1$ .

$z = \frac{7}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{7}{3}$

Decimal Form:

$z = 2.\overline{3}$

Mixed Number Form:

$z = 2 \frac{1}{3}$

Solve for z 7- square root of 3z+2=4

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