Solve for x ((2x+1.5)^3+61)^(1/3)-4=1

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

Step 1

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

Add $4$ to both sides of the equation.

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

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.

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

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

Step 4

Solve for $x$ .

Subtract $61$ from both sides of the equation.

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

Subtract $61$ from $125$ .

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

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

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

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

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

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

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

$2 x + 1.5 = 4$

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

Subtract $1.5$ from both sides of the equation.

$2 x = 4 - 1.5$

Subtract $1.5$ from $4$ .

$2 x = 2.5$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2.5$ by $2$ .

$x = 1.25$

Solve for x ((2x+1.5)^3+61)^(1/3)-4=1

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