Solve the Inequality for x -4(x+7)<3(x-2)

$- 4 (x + 7) < 3 (x - 2)$

Step 1

Simplify $- 4 (x + 7)$ .

Rewrite.

$0 + 0 - 4 (x + 7) < 3 (x - 2)$

Simplify by adding zeros.

$- 4 (x + 7) < 3 (x - 2)$

Apply the distributive property.

$- 4 x - 4 \cdot 7 < 3 (x - 2)$

Multiply $- 4$ by $7$ .

$- 4 x - 28 < 3 (x - 2)$

Step 2

Simplify $3 (x - 2)$ .

Apply the distributive property.

$- 4 x - 28 < 3 x + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$- 4 x - 28 < 3 x - 6$

Step 3

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

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

$- 4 x - 28 - 3 x < - 6$

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

$- 7 x - 28 < - 6$

Step 4

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

Add $28$ to both sides of the inequality.

$- 7 x < - 6 + 28$

Add $- 6$ and $28$ .

$- 7 x < 22$

Step 5

Divide each term in $- 7 x < 22$ by $- 7$ and simplify.

Divide each term in $- 7 x < 22$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} > \frac{22}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} > \frac{22}{- 7}$

Divide $x$ by $1$ .

$x > \frac{22}{- 7}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{22}{7}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{22}{7}$

Interval Notation:

$(- \frac{22}{7}, \infty)$

Solve the Inequality for x -4(x+7)<3(x-2)

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