Solve the Inequality for x -x>=-(-x+4)+3/4

$- x \geq - (- x + 4) + \frac{3}{4}$

Step 1

Simplify $- (- x + 4) + \frac{3}{4}$ .

Simplify each term.

Apply the distributive property.

$- x \geq - - x - 1 \cdot 4 + \frac{3}{4}$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$- x \geq 1 x - 1 \cdot 4 + \frac{3}{4}$

Multiply $x$ by $1$ .

$- x \geq x - 1 \cdot 4 + \frac{3}{4}$

Multiply $- 1$ by $4$ .

$- x \geq x - 4 + \frac{3}{4}$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- x \geq x - 4 \cdot \frac{4}{4} + \frac{3}{4}$

Combine $- 4$ and $\frac{4}{4}$ .

$- x \geq x + \frac{- 4 \cdot 4}{4} + \frac{3}{4}$

Combine the numerators over the common denominator.

$- x \geq x + \frac{- 4 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $- 4$ by $4$ .

$- x \geq x + \frac{- 16 + 3}{4}$

Add $- 16$ and $3$ .

$- x \geq x + \frac{- 13}{4}$

Move the negative in front of the fraction.

$- x \geq x - \frac{13}{4}$

Step 2

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

Subtract $x$ from both sides of the inequality.

$- x - x \geq - \frac{13}{4}$

Subtract $x$ from $- x$ .

$- 2 x \geq - \frac{13}{4}$

Step 3

Divide each term in $- 2 x \geq - \frac{13}{4}$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq - \frac{13}{4}$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{- \frac{13}{4}}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{- \frac{13}{4}}{- 2}$

Divide $x$ by $1$ .

$x \leq \frac{- \frac{13}{4}}{- 2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x \leq - \frac{13}{4} \cdot \frac{1}{- 2}$

Move the negative in front of the fraction.

$x \leq - \frac{13}{4} (- \frac{1}{2})$

Multiply $- \frac{13}{4} (- \frac{1}{2})$ .

Multiply $- 1$ by $- 1$ .

$x \leq 1 (\frac{13}{4}) \frac{1}{2}$

Multiply $\frac{13}{4}$ by $1$ .

$x \leq \frac{13}{4} \cdot \frac{1}{2}$

Multiply $\frac{13}{4}$ by $\frac{1}{2}$ .

$x \leq \frac{13}{4 \cdot 2}$

Multiply $4$ by $2$ .

$x \leq \frac{13}{8}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{13}{8}$

Interval Notation:

$(- \infty, \frac{13}{8}]$

Solve the Inequality for x -x>=-(-x+4)+3/4

Related Questions

Support LCMGCF.com by disabling your adblocker.