Finite Math Examples

$- \sqrt{3 x - 2} = 4$

Step 1

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

${(- \sqrt{3 x - 2})}^{2} = 4^{2}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

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

${(- {(3 x - 2)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

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

${(- 1)}^{2} {({(3 x - 2)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 2.2.1.2

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

$1 {({(3 x - 2)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 2.2.1.3

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

${({(3 x - 2)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 2.2.1.4

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

Tap for more steps...

Step 2.2.1.4.1

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

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 2.2.1.4.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.4.2.1

Cancel the common factor.

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 2.2.1.4.2.2

Rewrite the expression.

${(3 x - 2)}^{1} = 4^{2}$

Step 2.2.1.5

Simplify.

$3 x - 2 = 4^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

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

$3 x - 2 = 16$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $2$ to both sides of the equation.

$3 x = 16 + 2$

Step 3.1.2

Add $16$ and $2$ .

$3 x = 18$

Step 3.2

Divide each term in $3 x = 18$ by $3$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $3 x = 18$ by $3$ .

$\frac{3 x}{3} = \frac{18}{3}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{18}{3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{3}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $18$ by $3$ .

$x = 6$

Step 4

Exclude the solutions that do not make $- \sqrt{3 x - 2} = 4$ true.

$No solution$