Solve for x 5(6-3x)+6x<8(4+2x)

$5 (6 - 3 x) + 6 x < 8 (4 + 2 x)$

Step 1

Simplify $5 (6 - 3 x) + 6 x$ .

Simplify each term.

Apply the distributive property.

$5 \cdot 6 + 5 (- 3 x) + 6 x < 8 (4 + 2 x)$

Multiply $5$ by $6$ .

$30 + 5 (- 3 x) + 6 x < 8 (4 + 2 x)$

Multiply $- 3$ by $5$ .

$30 - 15 x + 6 x < 8 (4 + 2 x)$

Add $- 15 x$ and $6 x$ .

$30 - 9 x < 8 (4 + 2 x)$

Step 2

Simplify $8 (4 + 2 x)$ .

Apply the distributive property.

$30 - 9 x < 8 \cdot 4 + 8 (2 x)$

Multiply.

Multiply $8$ by $4$ .

$30 - 9 x < 32 + 8 (2 x)$

Multiply $2$ by $8$ .

$30 - 9 x < 32 + 16 x$

Step 3

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

Subtract $16 x$ from both sides of the inequality.

$30 - 9 x - 16 x < 32$

Subtract $16 x$ from $- 9 x$ .

$30 - 25 x < 32$

Step 4

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

Subtract $30$ from both sides of the inequality.

$- 25 x < 32 - 30$

Subtract $30$ from $32$ .

$- 25 x < 2$

Step 5

Divide each term in $- 25 x < 2$ by $- 25$ and simplify.

Divide each term in $- 25 x < 2$ by $- 25$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 25 x}{- 25} > \frac{2}{- 25}$

Simplify the left side.

Cancel the common factor of $- 25$ .

Cancel the common factor.

$\frac{- 25 x}{- 25} > \frac{2}{- 25}$

Divide $x$ by $1$ .

$x > \frac{2}{- 25}$

Simplify the right side.

Move the negative in front of the fraction.

$x > - \frac{2}{25}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{2}{25}$

Interval Notation:

$(- \frac{2}{25}, \infty)$

Solve for x 5(6-3x)+6x<8(4+2x)

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