Solve the System of Inequalities -8x+14>=60 OR -4x+50<58

$- 8 x + 14 \geq 60$ OR $- 4 x + 50 < 58$

Step 1

Solve $- 8 x + 14 \geq 60$ for $x$ .

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

Subtract $14$ from both sides of the inequality.

$- 8 x \geq 60 - 14$

Subtract $14$ from $60$ .

$- 8 x \geq 46$

Divide each term in $- 8 x \geq 46$ by $- 8$ and simplify.

Divide each term in $- 8 x \geq 46$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} \leq \frac{46}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} \leq \frac{46}{- 8}$

Divide $x$ by $1$ .

$x \leq \frac{46}{- 8}$

Simplify the right side.

Cancel the common factor of $46$ and $- 8$ .

Factor $2$ out of $46$ .

$x \leq \frac{2 (23)}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

$x \leq \frac{2 \cdot 23}{2 \cdot - 4}$

Cancel the common factor.

$x \leq \frac{2 \cdot 23}{2 \cdot - 4}$

Rewrite the expression.

$x \leq \frac{23}{- 4}$

Move the negative in front of the fraction.

$x \leq - \frac{23}{4}$

Step 2

Solve $- 4 x + 50 < 58$ for $x$ .

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

Subtract $50$ from both sides of the inequality.

$- 4 x < 58 - 50$

Subtract $50$ from $58$ .

$- 4 x < 8$

Divide each term in $- 4 x < 8$ by $- 4$ and simplify.

Divide each term in $- 4 x < 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{8}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{8}{- 4}$

Divide $x$ by $1$ .

$x > \frac{8}{- 4}$

Simplify the right side.

Divide $8$ by $- 4$ .

$x > - 2$

Step 3

Find the intersection of $x \leq - \frac{23}{4}$ and $x > - 2$ .

No solution

Solve the System of Inequalities -8x+14>=60 OR -4x+50<58

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