Algebra Examples

$400 > {(\frac{1}{20})}^{7 x + 8}$

Step 1

Apply the product rule to $\frac{1}{20}$ .

$400 > \frac{1^{7 x + 8}}{20^{7 x + 8}}$

Step 2

One to any power is one.

$400 > \frac{1}{20^{7 x + 8}}$

Step 3

Move $20^{7 x + 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$400 > 20^{- (7 x + 8)}$

Step 4

Create equivalent expressions in the equation that all have equal bases.

$20^{2} > 20^{- (7 x + 8)}$

Step 5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 > - (7 x + 8)$

Step 6

Solve for $x$ .

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Step 6.1

Rewrite so $x$ is on the left side of the inequality.

$- (7 x + 8) < 2$

Step 6.2

Simplify $- (7 x + 8)$ .

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Step 6.2.1

Apply the distributive property.

$- (7 x) - 1 \cdot 8 < 2$

Step 6.2.2

Multiply.

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Step 6.2.2.1

Multiply $7$ by $- 1$ .

$- 7 x - 1 \cdot 8 < 2$

Step 6.2.2.2

Multiply $- 1$ by $8$ .

$- 7 x - 8 < 2$

Step 6.3

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

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Step 6.3.1

Add $8$ to both sides of the inequality.

$- 7 x < 2 + 8$

Step 6.3.2

Add $2$ and $8$ .

$- 7 x < 10$

Step 6.4

Divide each term in $- 7 x < 10$ by $- 7$ and simplify.

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Step 6.4.1

Divide each term in $- 7 x < 10$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} > \frac{10}{- 7}$

Step 6.4.2

Simplify the left side.

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Step 6.4.2.1

Cancel the common factor of $- 7$ .

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Step 6.4.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} > \frac{10}{- 7}$

Step 6.4.2.1.2

Divide $x$ by $1$ .

$x > \frac{10}{- 7}$

Step 6.4.3

Simplify the right side.

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Step 6.4.3.1

Move the negative in front of the fraction.

$x > - \frac{10}{7}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{10}{7}$

Interval Notation:

$(- \frac{10}{7}, \infty)$

Step 8