Solve the Inequality for x x-4>=4x-14

$x - 4 \geq 4 x - 14$

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

Subtract $4 x$ from both sides of the inequality.

$x - 4 - 4 x \geq - 14$

Subtract $4 x$ from $x$ .

$- 3 x - 4 \geq - 14$

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

Add $4$ to both sides of the inequality.

$- 3 x \geq - 14 + 4$

Add $- 14$ and $4$ .

$- 3 x \geq - 10$

Divide each term in $- 3 x \geq - 10$ by $- 3$ and simplify.

Divide each term in $- 3 x \geq - 10$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \leq \frac{- 10}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \leq \frac{- 10}{- 3}$

Divide $x$ by $1$ .

$x \leq \frac{- 10}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \leq \frac{10}{3}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{10}{3}$

Interval Notation:

$(- \infty, \frac{10}{3}]$

Solve the Inequality for x x-4>=4x-14

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