Solve the Inequality for x 2-(4x-5)>3(x+4)-5

$2 - (4 x - 5) > 3 (x + 4) - 5$

Step 1

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

Simplify each term.

Apply the distributive property.

$2 - (4 x) - - 5 > 3 (x + 4) - 5$

Multiply $4$ by $- 1$ .

$2 - 4 x - - 5 > 3 (x + 4) - 5$

Multiply $- 1$ by $- 5$ .

$2 - 4 x + 5 > 3 (x + 4) - 5$

Add $2$ and $5$ .

$- 4 x + 7 > 3 (x + 4) - 5$

Step 2

Simplify $3 (x + 4) - 5$ .

Simplify each term.

Apply the distributive property.

$- 4 x + 7 > 3 x + 3 \cdot 4 - 5$

Multiply $3$ by $4$ .

$- 4 x + 7 > 3 x + 12 - 5$

Subtract $5$ from $12$ .

$- 4 x + 7 > 3 x + 7$

Step 3

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

Subtract $3 x$ from both sides of the inequality.

$- 4 x + 7 - 3 x > 7$

Subtract $3 x$ from $- 4 x$ .

$- 7 x + 7 > 7$

Step 4

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

Subtract $7$ from both sides of the inequality.

$- 7 x > 7 - 7$

Subtract $7$ from $7$ .

$- 7 x > 0$

Step 5

Divide each term in $- 7 x > 0$ by $- 7$ and simplify.

Divide each term in $- 7 x > 0$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} < \frac{0}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} < \frac{0}{- 7}$

Divide $x$ by $1$ .

$x < \frac{0}{- 7}$

Simplify the right side.

Divide $0$ by $- 7$ .

$x < 0$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 0$

Interval Notation:

$(- \infty, 0)$

Solve the Inequality for x 2-(4x-5)>3(x+4)-5

Related Questions

Support LCMGCF.com by disabling your adblocker.