Algebra Examples

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

Step 1

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

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Step 1.1

Add $3$ to both sides of the equation.

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

Step 1.2

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.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

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

Step 3.1.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

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

Step 3.1.1.1.2.2

Rewrite the expression.

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

Step 3.1.1.1.3

Cancel the common factor of $4$ .

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Step 3.1.1.1.3.1

Cancel the common factor.

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

Step 3.1.1.1.3.2

Rewrite the expression.

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

Step 3.1.1.2

Simplify.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

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

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Step 3.2.1.1

Simplify the expression.

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

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

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

Step 3.2.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.2.1

Cancel the common factor.

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

Step 3.2.1.2.2

Rewrite the expression.

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

Step 3.2.1.3

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

$2 x + 3 = 16$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $3$ from both sides of the equation.

$2 x = 16 - 3$

Step 4.1.2

Subtract $3$ from $16$ .

$2 x = 13$

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

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:

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