Solve the System of Inequalities -25x+175>225 ; AND , 5x-83>=-73

$- 25 x + 175 > 225$ ; AND , $5 x - 83 \geq - 73$

Step 1

Solve $- 25 x + 175 > 225$ for $x$ .

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

Subtract $175$ from both sides of the inequality.

$- 25 x > 225 - 175$

Subtract $175$ from $225$ .

$- 25 x > 50$

Divide each term in $- 25 x > 50$ by $- 25$ and simplify.

Divide each term in $- 25 x > 50$ by $- 25$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 25 x}{- 25} < \frac{50}{- 25}$

Simplify the left side.

Cancel the common factor of $- 25$ .

Cancel the common factor.

$\frac{- 25 x}{- 25} < \frac{50}{- 25}$

Divide $x$ by $1$ .

$x < \frac{50}{- 25}$

Simplify the right side.

Divide $50$ by $- 25$ .

$x < - 2$

Step 2

Solve $5 x - 83 \geq - 73$ for $x$ .

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

Add $83$ to both sides of the inequality.

$5 x \geq - 73 + 83$

Add $- 73$ and $83$ .

$5 x \geq 10$

Divide each term in $5 x \geq 10$ by $5$ and simplify.

Divide each term in $5 x \geq 10$ by $5$ .

$\frac{5 x}{5} \geq \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{10}{5}$

Divide $x$ by $1$ .

$x \geq \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$x \geq 2$

Step 3

Find the intersection of $x < - 2$ and $x \geq 2$ .

No solution

Solve the System of Inequalities -25x+175>225 ; AND , 5x-83>=-73

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