Algebra Examples

$7 - \frac{4}{5} x < \frac{3}{5}$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{4}{5}$ .

$7 - \frac{x \cdot 4}{5} < \frac{3}{5}$

Step 1.2

Move $4$ to the left of $x$ .

$7 - \frac{4 x}{5} < \frac{3}{5}$

Step 2

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

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Step 2.1

Subtract $7$ from both sides of the inequality.

$- \frac{4 x}{5} < \frac{3}{5} - 7$

Step 2.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{4 x}{5} < \frac{3}{5} - 7 \cdot \frac{5}{5}$

Step 2.3

Combine $- 7$ and $\frac{5}{5}$ .

$- \frac{4 x}{5} < \frac{3}{5} + \frac{- 7 \cdot 5}{5}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{4 x}{5} < \frac{3 - 7 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 7$ by $5$ .

$- \frac{4 x}{5} < \frac{3 - 35}{5}$

Step 2.5.2

Subtract $35$ from $3$ .

$- \frac{4 x}{5} < \frac{- 32}{5}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{4 x}{5} < - \frac{32}{5}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 4 x < - 32$

Step 4

Divide each term in $- 4 x < - 32$ by $- 4$ and simplify.

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Step 4.1

Divide each term in $- 4 x < - 32$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{- 32}{- 4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{- 32}{- 4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 32}{- 4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 32$ by $- 4$ .

$x > 8$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 8$

Interval Notation:

$(8, \infty)$