Solve for x 3 square root of 5x-2+1=7

$3 \sqrt{5 x - 2} + 1 = 7$

Step 1

Move all terms not containing $3 \sqrt{5 x - 2}$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$3 \sqrt{5 x - 2} = 7 - 1$

Subtract $1$ from $7$ .

$3 \sqrt{5 x - 2} = 6$

Step 2

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

${(3 \sqrt{5 x - 2})}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 2}$ as ${(5 x - 2)}^{\frac{1}{2}}$ .

${(3 {(5 x - 2)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${(3 {(5 x - 2)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $3 {(5 x - 2)}^{\frac{1}{2}}$ .

$3^{2} {({(5 x - 2)}^{\frac{1}{2}})}^{2} = 6^{2}$

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

$9 {({(5 x - 2)}^{\frac{1}{2}})}^{2} = 6^{2}$

Multiply the exponents in ${({(5 x - 2)}^{\frac{1}{2}})}^{2}$ .

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

$9 {(5 x - 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 {(5 x - 2)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

$9 {(5 x - 2)}^{1} = 6^{2}$

Simplify.

$9 (5 x - 2) = 6^{2}$

Apply the distributive property.

$9 (5 x) + 9 \cdot - 2 = 6^{2}$

Multiply.

Multiply $5$ by $9$ .

$45 x + 9 \cdot - 2 = 6^{2}$

Multiply $9$ by $- 2$ .

$45 x - 18 = 6^{2}$

Simplify the right side.

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

$45 x - 18 = 36$

Step 4

Solve for $x$ .

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

Add $18$ to both sides of the equation.

$45 x = 36 + 18$

Add $36$ and $18$ .

$45 x = 54$

Divide each term in $45 x = 54$ by $45$ and simplify.

Divide each term in $45 x = 54$ by $45$ .

$\frac{45 x}{45} = \frac{54}{45}$

Simplify the left side.

Cancel the common factor of $45$ .

Cancel the common factor.

$\frac{45 x}{45} = \frac{54}{45}$

Divide $x$ by $1$ .

$x = \frac{54}{45}$

Simplify the right side.

Cancel the common factor of $54$ and $45$ .

Factor $9$ out of $54$ .

$x = \frac{9 (6)}{45}$

Cancel the common factors.

Factor $9$ out of $45$ .

$x = \frac{9 \cdot 6}{9 \cdot 5}$

Cancel the common factor.

$x = \frac{9 \cdot 6}{9 \cdot 5}$

Rewrite the expression.

$x = \frac{6}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{5}$

Decimal Form:

$x = 1.2$

Mixed Number Form:

$x = 1 \frac{1}{5}$

Solve for x 3 square root of 5x-2+1=7

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