Solve the Inequality for x square root of 6x-2+1=-3

$\sqrt{6 x - 2} + 1 = - 3$

Step 1

Move all terms not containing $\sqrt{6 x - 2}$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$\sqrt{6 x - 2} = - 3 - 1$

Subtract $1$ from $- 3$ .

$\sqrt{6 x - 2} = - 4$

Step 2

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

${\sqrt{6 x - 2}}^{2} = {(- 4)}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x - 2}$ as ${(6 x - 2)}^{\frac{1}{2}}$ .

${({(6 x - 2)}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

Simplify the left side.

Simplify ${({(6 x - 2)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(6 x - 2)}^{\frac{1}{2}})}^{2}$ .

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

${(6 x - 2)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 x - 2)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Rewrite the expression.

${(6 x - 2)}^{1} = {(- 4)}^{2}$

Simplify.

$6 x - 2 = {(- 4)}^{2}$

Simplify the right side.

Raise $- 4$ to the power of $2$ .

$6 x - 2 = 16$

Step 4

Solve for $x$ .

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

Add $2$ to both sides of the equation.

$6 x = 16 + 2$

Add $16$ and $2$ .

$6 x = 18$

Divide each term in $6 x = 18$ by $6$ and simplify.

Divide each term in $6 x = 18$ by $6$ .

$\frac{6 x}{6} = \frac{18}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{18}{6}$

Divide $x$ by $1$ .

$x = \frac{18}{6}$

Simplify the right side.

Divide $18$ by $6$ .

$x = 3$

Step 5

Exclude the solutions that do not make $\sqrt{6 x - 2} + 1 = - 3$ true.

$No solution$

Solve the Inequality for x square root of 6x-2+1=-3

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