Solve for x -3/10x-7<1/2

$- \frac{3}{10} x - 7 < \frac{1}{2}$

Step 1

Simplify each term.

Combine $x$ and $\frac{3}{10}$ .

$- \frac{x \cdot 3}{10} - 7 < \frac{1}{2}$

Move $3$ to the left of $x$ .

$- \frac{3 x}{10} - 7 < \frac{1}{2}$

Step 2

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

Add $7$ to both sides of the inequality.

$- \frac{3 x}{10} < \frac{1}{2} + 7$

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 x}{10} < \frac{1}{2} + 7 \cdot \frac{2}{2}$

Combine $7$ and $\frac{2}{2}$ .

$- \frac{3 x}{10} < \frac{1}{2} + \frac{7 \cdot 2}{2}$

Combine the numerators over the common denominator.

$- \frac{3 x}{10} < \frac{1 + 7 \cdot 2}{2}$

Simplify the numerator.

Multiply $7$ by $2$ .

$- \frac{3 x}{10} < \frac{1 + 14}{2}$

Add $1$ and $14$ .

$- \frac{3 x}{10} < \frac{15}{2}$

Step 3

Divide each term in $- \frac{3 x}{10} < \frac{15}{2}$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{10} < \frac{15}{2}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{10}}{- 1} > \frac{\frac{15}{2}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{10}}{1} > \frac{\frac{15}{2}}{- 1}$

Divide $\frac{3 x}{10}$ by $1$ .

$\frac{3 x}{10} > \frac{\frac{15}{2}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{15}{2}}{- 1}$ .

$\frac{3 x}{10} > - 1 \cdot \frac{15}{2}$

Rewrite $- 1 \cdot \frac{15}{2}$ as $- \frac{15}{2}$ .

$\frac{3 x}{10} > - \frac{15}{2}$

Step 4

Multiply both sides by $10$ .

$\frac{3 x}{10} \cdot 10 > - \frac{15}{2} \cdot 10$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{3 x}{10} \cdot 10 > - \frac{15}{2} \cdot 10$

Rewrite the expression.

$3 x > - \frac{15}{2} \cdot 10$

Simplify the right side.

Simplify $- \frac{15}{2} \cdot 10$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{15}{2}$ into the numerator.

$3 x > \frac{- 15}{2} \cdot 10$

Factor $2$ out of $10$ .

$3 x > \frac{- 15}{2} \cdot (2 (5))$

Cancel the common factor.

$3 x > \frac{- 15}{2} \cdot (2 \cdot 5)$

Rewrite the expression.

$3 x > - 15 \cdot 5$

Multiply $- 15$ by $5$ .

$3 x > - 75$

Step 6

Divide each term in $3 x > - 75$ by $3$ and simplify.

Divide each term in $3 x > - 75$ by $3$ .

$\frac{3 x}{3} > \frac{- 75}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{- 75}{3}$

Divide $x$ by $1$ .

$x > \frac{- 75}{3}$

Simplify the right side.

Divide $- 75$ by $3$ .

$x > - 25$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > - 25$

Interval Notation:

$(- 25, \infty)$

Solve for x -3/10x-7<1/2

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