Solve the Inequality for x 2-3x<5(2-x)<=3(2-x)+10

$2 - 3 x < 5 (2 - x) \leq 3 (2 - x) + 10$

Step 1

Solve $2 - 3 x < 5 (2 - x)$ for $x$ .

Simplify $5 (2 - x)$ .

Rewrite.

$2 - 3 x < 0 + 0 + 5 (2 - x)$

Simplify by adding zeros.

$2 - 3 x < 5 (2 - x)$

Apply the distributive property.

$2 - 3 x < 5 \cdot 2 + 5 (- x)$

Multiply.

Multiply $5$ by $2$ .

$2 - 3 x < 10 + 5 (- x)$

Multiply $- 1$ by $5$ .

$2 - 3 x < 10 - 5 x$

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

Add $5 x$ to both sides of the inequality.

$2 - 3 x + 5 x < 10$

Add $- 3 x$ and $5 x$ .

$2 + 2 x < 10$

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

Subtract $2$ from both sides of the inequality.

$2 x < 10 - 2$

Subtract $2$ from $10$ .

$2 x < 8$

Divide each term in $2 x < 8$ by $2$ and simplify.

Divide each term in $2 x < 8$ by $2$ .

$\frac{2 x}{2} < \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{8}{2}$

Divide $x$ by $1$ .

$x < \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x < 4$

Step 2

Solve $5 (2 - x) \leq 3 (2 - x) + 10$ for $x$ .

Simplify $5 (2 - x)$ .

Rewrite.

$0 + 0 + 5 (2 - x) \leq 3 (2 - x) + 10$

Simplify by adding zeros.

$5 (2 - x) \leq 3 (2 - x) + 10$

Apply the distributive property.

$5 \cdot 2 + 5 (- x) \leq 3 (2 - x) + 10$

Multiply.

Multiply $5$ by $2$ .

$10 + 5 (- x) \leq 3 (2 - x) + 10$

Multiply $- 1$ by $5$ .

$10 - 5 x \leq 3 (2 - x) + 10$

Simplify $3 (2 - x) + 10$ .

Simplify each term.

Apply the distributive property.

$10 - 5 x \leq 3 \cdot 2 + 3 (- x) + 10$

Multiply $3$ by $2$ .

$10 - 5 x \leq 6 + 3 (- x) + 10$

Multiply $- 1$ by $3$ .

$10 - 5 x \leq 6 - 3 x + 10$

Add $6$ and $10$ .

$10 - 5 x \leq - 3 x + 16$

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

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

$10 - 5 x + 3 x \leq 16$

Add $- 5 x$ and $3 x$ .

$10 - 2 x \leq 16$

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

Subtract $10$ from both sides of the inequality.

$- 2 x \leq 16 - 10$

Subtract $10$ from $16$ .

$- 2 x \leq 6$

Divide each term in $- 2 x \leq 6$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq 6$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{6}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{6}{- 2}$

Simplify the right side.

Divide $6$ by $- 2$ .

$x \geq - 3$

Step 3

Find the intersection of $x < 4$ and $x \geq - 3$ .

$- 3 \leq x < 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x < 4$

Interval Notation:

$[- 3, 4)$

Step 5

Solve the Inequality for x 2-3x<5(2-x)<=3(2-x)+10

Related Questions

Support LCMGCF.com by disabling your adblocker.