Algebra Examples

${(7 x - 23)}^{\frac{1}{3}} = {(2 x + 17)}^{\frac{1}{3}}$

Step 1

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$7 x - 23 = 2 x + 17$

Step 2

Solve for $x$ .

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Step 2.1

Move all terms containing $x$ to the left side of the equation.

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Step 2.1.1

Subtract $2 x$ from both sides of the equation.

$7 x - 23 - 2 x = 17$

Step 2.1.2

Subtract $2 x$ from $7 x$ .

$5 x - 23 = 17$

Step 2.2

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

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Step 2.2.1

Add $23$ to both sides of the equation.

$5 x = 17 + 23$

Step 2.2.2

Add $17$ and $23$ .

$5 x = 40$

Step 2.3

Divide each term in $5 x = 40$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 x = 40$ by $5$ .

$\frac{5 x}{5} = \frac{40}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{40}{5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{40}{5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $40$ by $5$ .

$x = 8$