Algebra Examples

$7 \sqrt[3]{x - 3} \geq 21$

Step 1

To remove the radical on the left side of the inequality, cube both sides of the inequality.

${(7 \sqrt[3]{x - 3})}^{3} \geq 21^{3}$

Step 2

Simplify each side of the inequality.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 3}$ as ${(x - 3)}^{\frac{1}{3}}$ .

${(7 {(x - 3)}^{\frac{1}{3}})}^{3} \geq 21^{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

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

$7^{3} {({(x - 3)}^{\frac{1}{3}})}^{3} \geq 21^{3}$

Step 2.2.1.2

Raise $7$ to the power of $3$ .

$343 {({(x - 3)}^{\frac{1}{3}})}^{3} \geq 21^{3}$

Step 2.2.1.3

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

Tap for more steps...

Step 2.2.1.3.1

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

$343 {(x - 3)}^{\frac{1}{3} \cdot 3} \geq 21^{3}$

Step 2.2.1.3.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.3.2.1

Cancel the common factor.

$343 {(x - 3)}^{\frac{1}{3} \cdot 3} \geq 21^{3}$

Step 2.2.1.3.2.2

Rewrite the expression.

$343 {(x - 3)}^{1} \geq 21^{3}$

Step 2.2.1.4

Simplify.

$343 (x - 3) \geq 21^{3}$

Step 2.2.1.5

Apply the distributive property.

$343 x + 343 \cdot - 3 \geq 21^{3}$

Step 2.2.1.6

Multiply $343$ by $- 3$ .

$343 x - 1029 \geq 21^{3}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Raise $21$ to the power of $3$ .

$343 x - 1029 \geq 9261$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Add $1029$ to both sides of the inequality.

$343 x \geq 9261 + 1029$

Step 3.1.2

Add $9261$ and $1029$ .

$343 x \geq 10290$

Step 3.2

Divide each term in $343 x \geq 10290$ by $343$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $343 x \geq 10290$ by $343$ .

$\frac{343 x}{343} \geq \frac{10290}{343}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $343$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{343 x}{343} \geq \frac{10290}{343}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{10290}{343}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $10290$ by $343$ .

$x \geq 30$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 30$

Interval Notation:

$[30, \infty)$

Step 5