Algebra Examples

${({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3}} - 4 = 1$

Step 1

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

Tap for more steps...

Step 1.1

Add $4$ to both sides of the equation.

${({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3}} = 1 + 4$

Step 1.2

Add $1$ and $4$ .

${({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3}} = 5$

Step 2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${({({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3}})}^{3} = 5^{3}$

Step 3

Simplify the exponent.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify ${({({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.1.1.1

Multiply the exponents in ${({({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.1.1.1.1

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

${({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Step 3.1.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.1.2.1

Cancel the common factor.

${({(2 x + 1.5)}^{3} + 61)}^{\frac{1}{3} \cdot 3} = 5^{3}$

Step 3.1.1.1.2.2

Rewrite the expression.

${({(2 x + 1.5)}^{3} + 61)}^{1} = 5^{3}$

Step 3.1.1.2

Simplify.

${(2 x + 1.5)}^{3} + 61 = 5^{3}$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Raise $5$ to the power of $3$ .

${(2 x + 1.5)}^{3} + 61 = 125$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Subtract $61$ from both sides of the equation.

${(2 x + 1.5)}^{3} = 125 - 61$

Step 4.2

Subtract $61$ from $125$ .

${(2 x + 1.5)}^{3} = 64$

Step 4.3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$2 x + 1.5 = \sqrt[3]{64}$

Step 4.4

Simplify $\sqrt[3]{64}$ .

Tap for more steps...

Step 4.4.1

Rewrite $64$ as $4^{3}$ .

$2 x + 1.5 = \sqrt[3]{4^{3}}$

Step 4.4.2

Pull terms out from under the radical, assuming real numbers.

$2 x + 1.5 = 4$

Step 4.5

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

Tap for more steps...

Step 4.5.1

Subtract $1.5$ from both sides of the equation.

$2 x = 4 - 1.5$

Step 4.5.2

Subtract $1.5$ from $4$ .

$2 x = 2.5$

Step 4.6

Divide each term in $2 x = 2.5$ by $2$ and simplify.

Tap for more steps...

Step 4.6.1

Divide each term in $2 x = 2.5$ by $2$ .

$\frac{2 x}{2} = \frac{2.5}{2}$

Step 4.6.2

Simplify the left side.

Tap for more steps...

Step 4.6.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{2.5}{2}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{2.5}{2}$

Step 4.6.3

Simplify the right side.

Tap for more steps...

Step 4.6.3.1

Divide $2.5$ by $2$ .

$x = 1.25$