Solve the Inequality for x -4(x-2)+5<9

$- 4 (x - 2) + 5 < 9$

Step 1

Simplify $- 4 (x - 2) + 5$ .

Simplify each term.

Apply the distributive property.

$- 4 x - 4 \cdot - 2 + 5 < 9$

Multiply $- 4$ by $- 2$ .

$- 4 x + 8 + 5 < 9$

Add $8$ and $5$ .

$- 4 x + 13 < 9$

Step 2

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

Subtract $13$ from both sides of the inequality.

$- 4 x < 9 - 13$

Subtract $13$ from $9$ .

$- 4 x < - 4$

Step 3

Divide each term in $- 4 x < - 4$ by $- 4$ and simplify.

Divide each term in $- 4 x < - 4$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{- 4}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{- 4}{- 4}$

Divide $x$ by $1$ .

$x > \frac{- 4}{- 4}$

Simplify the right side.

Divide $- 4$ by $- 4$ .

$x > 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$

Solve the Inequality for x -4(x-2)+5<9

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