Solve the Inequality for x 2(5-2x)<=4-3x

$2 (5 - 2 x) \leq 4 - 3 x$

Simplify $2 (5 - 2 x)$ .

Rewrite.

$0 + 0 + 2 (5 - 2 x) \leq 4 - 3 x$

Simplify by adding zeros.

$2 (5 - 2 x) \leq 4 - 3 x$

Apply the distributive property.

$2 \cdot 5 + 2 (- 2 x) \leq 4 - 3 x$

Multiply.

Multiply $2$ by $5$ .

$10 + 2 (- 2 x) \leq 4 - 3 x$

Multiply $- 2$ by $2$ .

$10 - 4 x \leq 4 - 3 x$

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

Add $3 x$ to both sides of the inequality.

$10 - 4 x + 3 x \leq 4$

Add $- 4 x$ and $3 x$ .

$10 - x \leq 4$

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

Subtract $10$ from both sides of the inequality.

$- x \leq 4 - 10$

Subtract $10$ from $4$ .

$- x \leq - 6$

Divide each term in $- x \leq - 6$ by $- 1$ and simplify.

Divide each term in $- x \leq - 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x \geq 6$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 6$

Interval Notation:

$[6, \infty)$

Solve the Inequality for x 2(5-2x)<=4-3x

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