Solve the Inequality for x -5x+4<=-4(x-1)

$- 5 x + 4 \leq - 4 (x - 1)$

Simplify $- 4 (x - 1)$ .

Rewrite.

$- 5 x + 4 \leq 0 + 0 - 4 (x - 1)$

Simplify by adding zeros.

$- 5 x + 4 \leq - 4 (x - 1)$

Apply the distributive property.

$- 5 x + 4 \leq - 4 x - 4 \cdot - 1$

Multiply $- 4$ by $- 1$ .

$- 5 x + 4 \leq - 4 x + 4$

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

Add $4 x$ to both sides of the inequality.

$- 5 x + 4 + 4 x \leq 4$

Add $- 5 x$ and $4 x$ .

$- x + 4 \leq 4$

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

Subtract $4$ from both sides of the inequality.

$- x \leq 4 - 4$

Subtract $4$ from $4$ .

$- x \leq 0$

Divide each term in $- x \leq 0$ by $- 1$ and simplify.

Divide each term in $- x \leq 0$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{0}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x \geq 0$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 0$

Interval Notation:

$[0, \infty)$

Solve the Inequality for x -5x+4<=-4(x-1)

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