Solve the Inequality for x 10(x+4)<8x-(x+2)

$10 (x + 4) < 8 x - (x + 2)$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$8 x - (x + 2) > 10 (x + 4)$

Step 2

Simplify $8 x - (x + 2)$ .

Simplify each term.

Apply the distributive property.

$8 x - x - 1 \cdot 2 > 10 (x + 4)$

Multiply $- 1$ by $2$ .

$8 x - x - 2 > 10 (x + 4)$

Subtract $x$ from $8 x$ .

$7 x - 2 > 10 (x + 4)$

Step 3

Simplify $10 (x + 4)$ .

Apply the distributive property.

$7 x - 2 > 10 x + 10 \cdot 4$

Multiply $10$ by $4$ .

$7 x - 2 > 10 x + 40$

Step 4

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

Subtract $10 x$ from both sides of the inequality.

$7 x - 2 - 10 x > 40$

Subtract $10 x$ from $7 x$ .

$- 3 x - 2 > 40$

Step 5

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

Add $2$ to both sides of the inequality.

$- 3 x > 40 + 2$

Add $40$ and $2$ .

$- 3 x > 42$

Step 6

Divide each term in $- 3 x > 42$ by $- 3$ and simplify.

Divide each term in $- 3 x > 42$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{42}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{42}{- 3}$

Divide $x$ by $1$ .

$x < \frac{42}{- 3}$

Simplify the right side.

Divide $42$ by $- 3$ .

$x < - 14$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x < - 14$

Interval Notation:

$(- \infty, - 14)$

Solve the Inequality for x 10(x+4)<8x-(x+2)

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