Solve for x 4(3-2x)+3x<6(4+2x)

$4 (3 - 2 x) + 3 x < 6 (4 + 2 x)$

Step 1

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

Simplify each term.

Apply the distributive property.

$4 \cdot 3 + 4 (- 2 x) + 3 x < 6 (4 + 2 x)$

Multiply $4$ by $3$ .

$12 + 4 (- 2 x) + 3 x < 6 (4 + 2 x)$

Multiply $- 2$ by $4$ .

$12 - 8 x + 3 x < 6 (4 + 2 x)$

Add $- 8 x$ and $3 x$ .

$12 - 5 x < 6 (4 + 2 x)$

Step 2

Simplify $6 (4 + 2 x)$ .

Apply the distributive property.

$12 - 5 x < 6 \cdot 4 + 6 (2 x)$

Multiply.

Multiply $6$ by $4$ .

$12 - 5 x < 24 + 6 (2 x)$

Multiply $2$ by $6$ .

$12 - 5 x < 24 + 12 x$

Step 3

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

Subtract $12 x$ from both sides of the inequality.

$12 - 5 x - 12 x < 24$

Subtract $12 x$ from $- 5 x$ .

$12 - 17 x < 24$

Step 4

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

Subtract $12$ from both sides of the inequality.

$- 17 x < 24 - 12$

Subtract $12$ from $24$ .

$- 17 x < 12$

Step 5

Divide each term in $- 17 x < 12$ by $- 17$ and simplify.

Divide each term in $- 17 x < 12$ by $- 17$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 17 x}{- 17} > \frac{12}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 x}{- 17} > \frac{12}{- 17}$

Divide $x$ by $1$ .

$x > \frac{12}{- 17}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{12}{17}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{12}{17}$

Interval Notation:

$(- \frac{12}{17}, \infty)$

Solve for x 4(3-2x)+3x<6(4+2x)

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