Algebra Examples

$1 > - (x - \frac{5}{2}) - 4 x$

Step 1

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

$- (x - \frac{5}{2}) - 4 x < 1$

Step 2

Simplify $- (x - \frac{5}{2}) - 4 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- x - - \frac{5}{2} - 4 x < 1$

Step 2.1.2

Multiply $- - \frac{5}{2}$ .

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Step 2.1.2.1

Multiply $- 1$ by $- 1$ .

$- x + 1 (\frac{5}{2}) - 4 x < 1$

Step 2.1.2.2

Multiply $\frac{5}{2}$ by $1$ .

$- x + \frac{5}{2} - 4 x < 1$

Step 2.2

Subtract $4 x$ from $- x$ .

$- 5 x + \frac{5}{2} < 1$

Step 3

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

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Step 3.1

Subtract $\frac{5}{2}$ from both sides of the inequality.

$- 5 x < 1 - \frac{5}{2}$

Step 3.2

Write $1$ as a fraction with a common denominator.

$- 5 x < \frac{2}{2} - \frac{5}{2}$

Step 3.3

Combine the numerators over the common denominator.

$- 5 x < \frac{2 - 5}{2}$

Step 3.4

Subtract $5$ from $2$ .

$- 5 x < \frac{- 3}{2}$

Step 3.5

Move the negative in front of the fraction.

$- 5 x < - \frac{3}{2}$

Step 4

Divide each term in $- 5 x < - \frac{3}{2}$ by $- 5$ and simplify.

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Step 4.1

Divide each term in $- 5 x < - \frac{3}{2}$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} > \frac{- \frac{3}{2}}{- 5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} > \frac{- \frac{3}{2}}{- 5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{- \frac{3}{2}}{- 5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$x > - \frac{3}{2} \cdot \frac{1}{- 5}$

Step 4.3.2

Move the negative in front of the fraction.

$x > - \frac{3}{2} (- \frac{1}{5})$

Step 4.3.3

Multiply $- \frac{3}{2} (- \frac{1}{5})$ .

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Step 4.3.3.1

Multiply $- 1$ by $- 1$ .

$x > 1 (\frac{3}{2}) \frac{1}{5}$

Step 4.3.3.2

Multiply $\frac{3}{2}$ by $1$ .

$x > \frac{3}{2} \cdot \frac{1}{5}$

Step 4.3.3.3

Multiply $\frac{3}{2}$ by $\frac{1}{5}$ .

$x > \frac{3}{2 \cdot 5}$

Step 4.3.3.4

Multiply $2$ by $5$ .

$x > \frac{3}{10}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{3}{10}$

Interval Notation:

$(\frac{3}{10}, \infty)$