Solve the Inequality for x x-4>4(x-1)

$x - 4 > 4 (x - 1)$

Step 1

Simplify $4 (x - 1)$ .

Rewrite.

$x - 4 > 0 + 0 + 4 (x - 1)$

Simplify by adding zeros.

$x - 4 > 4 (x - 1)$

Apply the distributive property.

$x - 4 > 4 x + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$x - 4 > 4 x - 4$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$x - 4 - 4 x > - 4$

Subtract $4 x$ from $x$ .

$- 3 x - 4 > - 4$

Step 3

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

Add $4$ to both sides of the inequality.

$- 3 x > - 4 + 4$

Add $- 4$ and $4$ .

$- 3 x > 0$

Step 4

Divide each term in $- 3 x > 0$ by $- 3$ and simplify.

Divide each term in $- 3 x > 0$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{0}{- 3}$

Divide $x$ by $1$ .

$x < \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$x < 0$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 0$

Interval Notation:

$(- \infty, 0)$

Solve the Inequality for x x-4>4(x-1)

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