Solve the Inequality for x 3(4-5x)>8x-149

$3 (4 - 5 x) > 8 x - 149$

Step 1

Simplify $3 (4 - 5 x)$ .

Rewrite.

$0 + 0 + 3 (4 - 5 x) > 8 x - 149$

Simplify by adding zeros.

$3 (4 - 5 x) > 8 x - 149$

Apply the distributive property.

$3 \cdot 4 + 3 (- 5 x) > 8 x - 149$

Multiply.

Multiply $3$ by $4$ .

$12 + 3 (- 5 x) > 8 x - 149$

Multiply $- 5$ by $3$ .

$12 - 15 x > 8 x - 149$

Step 2

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

Subtract $8 x$ from both sides of the inequality.

$12 - 15 x - 8 x > - 149$

Subtract $8 x$ from $- 15 x$ .

$12 - 23 x > - 149$

Step 3

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

Subtract $12$ from both sides of the inequality.

$- 23 x > - 149 - 12$

Subtract $12$ from $- 149$ .

$- 23 x > - 161$

Step 4

Divide each term in $- 23 x > - 161$ by $- 23$ and simplify.

Divide each term in $- 23 x > - 161$ by $- 23$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 23 x}{- 23} < \frac{- 161}{- 23}$

Simplify the left side.

Cancel the common factor of $- 23$ .

Cancel the common factor.

$\frac{- 23 x}{- 23} < \frac{- 161}{- 23}$

Divide $x$ by $1$ .

$x < \frac{- 161}{- 23}$

Simplify the right side.

Divide $- 161$ by $- 23$ .

$x < 7$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 7$

Interval Notation:

$(- \infty, 7)$

Solve the Inequality for x 3(4-5x)>8x-149

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