Solve the Inequality for x x/2+1>-1+x/5

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

Step 1

Move all terms containing $x$ to the left side of the inequality.

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

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

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

To write $- \frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $5$ .

$\frac{x \cdot 5}{10} - \frac{x}{5} \cdot \frac{2}{2} + 1 > - 1$

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

$\frac{x \cdot 5}{10} - \frac{x \cdot 2}{5 \cdot 2} + 1 > - 1$

Multiply $5$ by $2$ .

$\frac{x \cdot 5}{10} - \frac{x \cdot 2}{10} + 1 > - 1$

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - x \cdot 2}{10} + 1 > - 1$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 5 - x \cdot 2$ .

Factor $x$ out of $x \cdot 5$ .

$\frac{x (5) - x \cdot 2}{10} + 1 > - 1$

Factor $x$ out of $- x \cdot 2$ .

$\frac{x (5) + x (- 1 \cdot 2)}{10} + 1 > - 1$

Factor $x$ out of $x (5) + x (- 1 \cdot 2)$ .

$\frac{x (5 - 1 \cdot 2)}{10} + 1 > - 1$

Multiply $- 1$ by $2$ .

$\frac{x (5 - 2)}{10} + 1 > - 1$

Subtract $2$ from $5$ .

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

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

$\frac{3 x}{10} + 1 > - 1$

Step 2

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

Subtract $1$ from both sides of the inequality.

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

Subtract $1$ from $- 1$ .

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

Step 3

Multiply both sides by $10$ .

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

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

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

Rewrite the expression.

$3 x > - 2 \cdot 10$

Simplify the right side.

Multiply $- 2$ by $10$ .

$3 x > - 20$

Step 5

Divide each term in $3 x > - 20$ by $3$ and simplify.

Divide each term in $3 x > - 20$ by $3$ .

$\frac{3 x}{3} > \frac{- 20}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{- 20}{3}$

Divide $x$ by $1$ .

$x > \frac{- 20}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{20}{3}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{20}{3}$

Interval Notation:

$(- \frac{20}{3}, \infty)$

Solve the Inequality for x x/2+1>-1+x/5

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