Algebra Examples

$2 {(6 x - 7)}^{\frac{1}{3}} - 5 = 5$

Step 1

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

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Step 1.1

Add $5$ to both sides of the equation.

$2 {(6 x - 7)}^{\frac{1}{3}} = 5 + 5$

Step 1.2

Add $5$ and $5$ .

$2 {(6 x - 7)}^{\frac{1}{3}} = 10$

Step 2

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

${(2 {(6 x - 7)}^{\frac{1}{3}})}^{3} = 10^{3}$

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 ${(2 {(6 x - 7)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1

Apply the product rule to $2 {(6 x - 7)}^{\frac{1}{3}}$ .

$2^{3} {({(6 x - 7)}^{\frac{1}{3}})}^{3} = 10^{3}$

Step 3.1.1.2

Raise $2$ to the power of $3$ .

$8 {({(6 x - 7)}^{\frac{1}{3}})}^{3} = 10^{3}$

Step 3.1.1.3

Multiply the exponents in ${({(6 x - 7)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.3.1

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

$8 {(6 x - 7)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Step 3.1.1.3.2

Cancel the common factor of $3$ .

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Step 3.1.1.3.2.1

Cancel the common factor.

$8 {(6 x - 7)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Step 3.1.1.3.2.2

Rewrite the expression.

$8 {(6 x - 7)}^{1} = 10^{3}$

Step 3.1.1.4

Simplify.

$8 (6 x - 7) = 10^{3}$

Step 3.1.1.5

Apply the distributive property.

$8 (6 x) + 8 \cdot - 7 = 10^{3}$

Step 3.1.1.6

Multiply.

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Step 3.1.1.6.1

Multiply $6$ by $8$ .

$48 x + 8 \cdot - 7 = 10^{3}$

Step 3.1.1.6.2

Multiply $8$ by $- 7$ .

$48 x - 56 = 10^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $10$ to the power of $3$ .

$48 x - 56 = 1000$

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

Add $56$ to both sides of the equation.

$48 x = 1000 + 56$

Step 4.1.2

Add $1000$ and $56$ .

$48 x = 1056$

Step 4.2

Divide each term in $48 x = 1056$ by $48$ and simplify.

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Step 4.2.1

Divide each term in $48 x = 1056$ by $48$ .

$\frac{48 x}{48} = \frac{1056}{48}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $48$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{48 x}{48} = \frac{1056}{48}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1056}{48}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $1056$ by $48$ .

$x = 22$