Solve the Inequality for x 4(2-x)>-2x-3(4x+1)

$4 (2 - x) > - 2 x - 3 (4 x + 1)$

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

$- 2 x - 3 (4 x + 1) < 4 (2 - x)$

Simplify $- 2 x - 3 (4 x + 1)$ .

Simplify each term.

Apply the distributive property.

$- 2 x - 3 (4 x) - 3 \cdot 1 < 4 (2 - x)$

Multiply $4$ by $- 3$ .

$- 2 x - 12 x - 3 \cdot 1 < 4 (2 - x)$

Multiply $- 3$ by $1$ .

$- 2 x - 12 x - 3 < 4 (2 - x)$

Subtract $12 x$ from $- 2 x$ .

$- 14 x - 3 < 4 (2 - x)$

Simplify $4 (2 - x)$ .

Apply the distributive property.

$- 14 x - 3 < 4 \cdot 2 + 4 (- x)$

Multiply.

Multiply $4$ by $2$ .

$- 14 x - 3 < 8 + 4 (- x)$

Multiply $- 1$ by $4$ .

$- 14 x - 3 < 8 - 4 x$

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

Add $4 x$ to both sides of the inequality.

$- 14 x - 3 + 4 x < 8$

Add $- 14 x$ and $4 x$ .

$- 10 x - 3 < 8$

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

Add $3$ to both sides of the inequality.

$- 10 x < 8 + 3$

Add $8$ and $3$ .

$- 10 x < 11$

Divide each term in $- 10 x < 11$ by $- 10$ and simplify.

Divide each term in $- 10 x < 11$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 x}{- 10} > \frac{11}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} > \frac{11}{- 10}$

Divide $x$ by $1$ .

$x > \frac{11}{- 10}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{11}{10}$

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{11}{10}$

Interval Notation:

$(- \frac{11}{10}, \infty)$

Solve the Inequality for x 4(2-x)>-2x-3(4x+1)

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