Solve the System of Inequalities 12x+7<-11 ; AND , 5x-8>=40

$12 x + 7 < - 11$ ; AND , $5 x - 8 \geq 40$

Step 1

Solve $12 x + 7 < - 11$ for $x$ .

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

Subtract $7$ from both sides of the inequality.

$12 x < - 11 - 7$

Subtract $7$ from $- 11$ .

$12 x < - 18$

Divide each term in $12 x < - 18$ by $12$ and simplify.

Divide each term in $12 x < - 18$ by $12$ .

$\frac{12 x}{12} < \frac{- 18}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} < \frac{- 18}{12}$

Divide $x$ by $1$ .

$x < \frac{- 18}{12}$

Simplify the right side.

Cancel the common factor of $- 18$ and $12$ .

Factor $6$ out of $- 18$ .

$x < \frac{6 (- 3)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$x < \frac{6 \cdot - 3}{6 \cdot 2}$

Cancel the common factor.

$x < \frac{6 \cdot - 3}{6 \cdot 2}$

Rewrite the expression.

$x < \frac{- 3}{2}$

Move the negative in front of the fraction.

$x < - \frac{3}{2}$

Step 2

Solve $5 x - 8 \geq 40$ for $x$ .

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

Add $8$ to both sides of the inequality.

$5 x \geq 40 + 8$

Add $40$ and $8$ .

$5 x \geq 48$

Divide each term in $5 x \geq 48$ by $5$ and simplify.

Divide each term in $5 x \geq 48$ by $5$ .

$\frac{5 x}{5} \geq \frac{48}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{48}{5}$

Divide $x$ by $1$ .

$x \geq \frac{48}{5}$

Step 3

Find the intersection of $x < - \frac{3}{2}$ and $x \geq \frac{48}{5}$ .

No solution

Solve the System of Inequalities 12x+7<-11 ; AND , 5x-8>=40

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