Algebra Examples

${(2 x + 3)}^{3} - 7 = 1$

Step 1

Add $7$ to both sides of the equation.

${(2 x + 3)}^{3} = 1 + 7$

Step 2

Add $1$ and $7$ .

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

Step 3

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

$2 x + 3 = \sqrt[3]{8}$

Step 4

Simplify $\sqrt[3]{8}$ .

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Step 4.1

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

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

Step 4.2

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

$2 x + 3 = 2$

Step 5

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

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Step 5.1

Subtract $3$ from both sides of the equation.

$2 x = 2 - 3$

Step 5.2

Subtract $3$ from $2$ .

$2 x = - 1$

Step 6

Divide each term in $2 x = - 1$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 x = - 1$ by $2$ .

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

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

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

Step 6.2.1.2

Divide $x$ by $1$ .

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

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$