Solve for x 5(3-x)-4(2-3x)>2

$5 (3 - x) - 4 (2 - 3 x) > 2$

Step 1

Simplify $5 (3 - x) - 4 (2 - 3 x)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $3$ .

$15 + 5 (- x) - 4 (2 - 3 x) > 2$

Multiply $- 1$ by $5$ .

$15 - 5 x - 4 (2 - 3 x) > 2$

Apply the distributive property.

$15 - 5 x - 4 \cdot 2 - 4 (- 3 x) > 2$

Multiply $- 4$ by $2$ .

$15 - 5 x - 8 - 4 (- 3 x) > 2$

Multiply $- 3$ by $- 4$ .

$15 - 5 x - 8 + 12 x > 2$

Simplify by adding terms.

Subtract $8$ from $15$ .

$- 5 x + 7 + 12 x > 2$

Add $- 5 x$ and $12 x$ .

$7 x + 7 > 2$

Step 2

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

Subtract $7$ from both sides of the inequality.

$7 x > 2 - 7$

Subtract $7$ from $2$ .

$7 x > - 5$

Step 3

Divide each term in $7 x > - 5$ by $7$ and simplify.

Divide each term in $7 x > - 5$ by $7$ .

$\frac{7 x}{7} > \frac{- 5}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} > \frac{- 5}{7}$

Divide $x$ by $1$ .

$x > \frac{- 5}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{5}{7}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{5}{7}$

Interval Notation:

$(- \frac{5}{7}, \infty)$

Solve for x 5(3-x)-4(2-3x)>2

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