Solve for x (2x+3)^(3/4)-3=5

${(2 x + 3)}^{\frac{3}{4}} - 3 = 5$

Step 1

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

Add $3$ to both sides of the equation.

${(2 x + 3)}^{\frac{3}{4}} = 5 + 3$

Add $5$ and $3$ .

${(2 x + 3)}^{\frac{3}{4}} = 8$

Step 2

Raise each side of the equation to the power of $\frac{4}{3}$ to eliminate the fractional exponent on the left side.

${({(2 x + 3)}^{\frac{3}{4}})}^{\frac{4}{3}} = 8^{\frac{4}{3}}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${({(2 x + 3)}^{\frac{3}{4}})}^{\frac{4}{3}}$ .

Multiply the exponents in ${({(2 x + 3)}^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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

${(2 x + 3)}^{\frac{3}{4} \cdot \frac{4}{3}} = 8^{\frac{4}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x + 3)}^{\frac{3}{4} \cdot \frac{4}{3}} = 8^{\frac{4}{3}}$

Rewrite the expression.

${(2 x + 3)}^{\frac{1}{4} \cdot 4} = 8^{\frac{4}{3}}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(2 x + 3)}^{\frac{1}{4} \cdot 4} = 8^{\frac{4}{3}}$

Rewrite the expression.

${(2 x + 3)}^{1} = 8^{\frac{4}{3}}$

Simplify.

$2 x + 3 = 8^{\frac{4}{3}}$

Simplify the right side.

Simplify $8^{\frac{4}{3}}$ .

Simplify the expression.

Rewrite $8$ as $2^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

$2 x + 3 = 16$

Step 4

Solve for $x$ .

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

Subtract $3$ from both sides of the equation.

$2 x = 16 - 3$

Subtract $3$ from $16$ .

$2 x = 13$

Divide each term in $2 x = 13$ by $2$ and simplify.

Divide each term in $2 x = 13$ by $2$ .

$\frac{2 x}{2} = \frac{13}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{13}{2}$

Divide $x$ by $1$ .

$x = \frac{13}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{2}$

Decimal Form:

$x = 6.5$

Mixed Number Form:

$x = 6 \frac{1}{2}$

Solve for x (2x+3)^(3/4)-3=5

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