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

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

Step 1

Simplify $1 - (- x + \frac{5}{2})$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the expression.

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

$5 + 2 x \geq x + \frac{2}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$5 + 2 x \geq x + \frac{2 - 5}{2}$

Subtract $5$ from $2$ .

$5 + 2 x \geq x + \frac{- 3}{2}$

Move the negative in front of the fraction.

$5 + 2 x \geq x - \frac{3}{2}$

Step 2

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

Subtract $x$ from both sides of the inequality.

$5 + 2 x - x \geq - \frac{3}{2}$

Subtract $x$ from $2 x$ .

$5 + x \geq - \frac{3}{2}$

Step 3

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

Subtract $5$ from both sides of the inequality.

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

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

$x \geq - \frac{3}{2} - 5 \cdot \frac{2}{2}$

Combine $- 5$ and $\frac{2}{2}$ .

$x \geq - \frac{3}{2} + \frac{- 5 \cdot 2}{2}$

Combine the numerators over the common denominator.

$x \geq \frac{- 3 - 5 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 5$ by $2$ .

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

Subtract $10$ from $- 3$ .

$x \geq \frac{- 13}{2}$

Move the negative in front of the fraction.

$x \geq - \frac{13}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{13}{2}$

Interval Notation:

$[- \frac{13}{2}, \infty)$

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

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