Solve the Inequality for x (x+14)/2<=4x

$\frac{x + 14}{2} \leq 4 x$

Step 1

Multiply both sides by $2$ .

$\frac{x + 14}{2} \cdot 2 \leq 4 x \cdot 2$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x + 14}{2} \cdot 2 \leq 4 x \cdot 2$

Rewrite the expression.

$x + 14 \leq 4 x \cdot 2$

Simplify the right side.

Multiply $2$ by $4$ .

$x + 14 \leq 8 x$

Step 3

Solve for $x$ .

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

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

$x + 14 - 8 x \leq 0$

Subtract $8 x$ from $x$ .

$- 7 x + 14 \leq 0$

Subtract $14$ from both sides of the inequality.

$- 7 x \leq - 14$

Divide each term in $- 7 x \leq - 14$ by $- 7$ and simplify.

Divide each term in $- 7 x \leq - 14$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 x}{- 7} \geq \frac{- 14}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} \geq \frac{- 14}{- 7}$

Divide $x$ by $1$ .

$x \geq \frac{- 14}{- 7}$

Simplify the right side.

Divide $- 14$ by $- 7$ .

$x \geq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$

Solve the Inequality for x (x+14)/2<=4x

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