Solve the System of Inequalities -18x+21>-15 ; OR , 20x-13>=27

$- 18 x + 21 > - 15$ ; OR , $20 x - 13 \geq 27$

Step 1

Solve $- 18 x + 21 > - 15$ for $x$ .

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

Subtract $21$ from both sides of the inequality.

$- 18 x > - 15 - 21$

Subtract $21$ from $- 15$ .

$- 18 x > - 36$

Divide each term in $- 18 x > - 36$ by $- 18$ and simplify.

Divide each term in $- 18 x > - 36$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 x}{- 18} < \frac{- 36}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 x}{- 18} < \frac{- 36}{- 18}$

Divide $x$ by $1$ .

$x < \frac{- 36}{- 18}$

Simplify the right side.

Divide $- 36$ by $- 18$ .

$x < 2$

Step 2

Solve $20 x - 13 \geq 27$ for $x$ .

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

Add $13$ to both sides of the inequality.

$20 x \geq 27 + 13$

Add $27$ and $13$ .

$20 x \geq 40$

Divide each term in $20 x \geq 40$ by $20$ and simplify.

Divide each term in $20 x \geq 40$ by $20$ .

$\frac{20 x}{20} \geq \frac{40}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 x}{20} \geq \frac{40}{20}$

Divide $x$ by $1$ .

$x \geq \frac{40}{20}$

Simplify the right side.

Divide $40$ by $20$ .

$x \geq 2$

Step 3

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

No solution

Solve the System of Inequalities -18x+21>-15 ; OR , 20x-13>=27

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