Solve for w -3(4w-1)>18

$- 3 (4 w - 1) > 18$

Step 1

Divide each term in $- 3 (4 w - 1) > 18$ by $- 3$ and simplify.

Divide each term in $- 3 (4 w - 1) > 18$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 (4 w - 1)}{- 3} < \frac{18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 (4 w - 1)}{- 3} < \frac{18}{- 3}$

Divide $4 w - 1$ by $1$ .

$4 w - 1 < \frac{18}{- 3}$

Simplify the right side.

Divide $18$ by $- 3$ .

$4 w - 1 < - 6$

Step 2

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

Add $1$ to both sides of the inequality.

$4 w < - 6 + 1$

Add $- 6$ and $1$ .

$4 w < - 5$

Step 3

Divide each term in $4 w < - 5$ by $4$ and simplify.

Divide each term in $4 w < - 5$ by $4$ .

$\frac{4 w}{4} < \frac{- 5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 w}{4} < \frac{- 5}{4}$

Divide $w$ by $1$ .

$w < \frac{- 5}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$w < - \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w < - \frac{5}{4}$

Interval Notation:

$(- \infty, - \frac{5}{4})$

Solve for w -3(4w-1)>18

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