Solve the Inequality for u 4u-6>=6u-20

$4 u - 6 \geq 6 u - 20$

Step 1

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

Subtract $6 u$ from both sides of the inequality.

$4 u - 6 - 6 u \geq - 20$

Subtract $6 u$ from $4 u$ .

$- 2 u - 6 \geq - 20$

Step 2

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

Add $6$ to both sides of the inequality.

$- 2 u \geq - 20 + 6$

Add $- 20$ and $6$ .

$- 2 u \geq - 14$

Step 3

Divide each term in $- 2 u \geq - 14$ by $- 2$ and simplify.

Divide each term in $- 2 u \geq - 14$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 u}{- 2} \leq \frac{- 14}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 u}{- 2} \leq \frac{- 14}{- 2}$

Divide $u$ by $1$ .

$u \leq \frac{- 14}{- 2}$

Simplify the right side.

Divide $- 14$ by $- 2$ .

$u \leq 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$u \leq 7$

Interval Notation:

$(- \infty, 7]$

Solve the Inequality for u 4u-6>=6u-20

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