Algebra Examples

$\frac{1}{2} > - 2 x + \frac{7}{2}$

Step 1

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

$- 2 x + \frac{7}{2} < \frac{1}{2}$

Step 2

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

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Step 2.1

Subtract $\frac{7}{2}$ from both sides of the inequality.

$- 2 x < \frac{1}{2} - \frac{7}{2}$

Step 2.2

Combine the numerators over the common denominator.

$- 2 x < \frac{1 - 7}{2}$

Step 2.3

Subtract $7$ from $1$ .

$- 2 x < \frac{- 6}{2}$

Step 2.4

Divide $- 6$ by $2$ .

$- 2 x < - 3$

Step 3

Divide each term in $- 2 x < - 3$ by $- 2$ and simplify.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

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

Step 4