Question

$\frac{x - 6}{4} \leq -2$ or $x + 5 - 7x < 11$
plot the endpoints. select an endpoint to change it from closed to open. select the middle of
a segment, ray, or line to delete it.
-6 -5 -4 -3 -2 -1 0 1
submit
work it out
not feeling ready yet? these can help:
solve linear inequalities graph inequalities (100)

Explanation:

Step1: Solve first inequality

Multiply both sides by 4:
$$x - 6 \leq -2 \times 4$$
Simplify and isolate $x$:
$$x \leq -8 + 6$$
$$x \leq -2$$

Step2: Solve second inequality

Combine like terms:
$$-6x + 5 < 11$$
Isolate the $x$-term:
$$-6x < 11 - 5$$
Divide by -6 (reverse inequality):
$$x > \frac{6}{-6}$$
$$x > -1$$

Answer:

The solution set is $x \leq -2$ or $x > -1$.

• For $x \leq -2$: Plot a closed endpoint at $-2$, draw a ray extending left from $-2$.
• For $x > -1$: Plot an open endpoint at $-1$, draw a ray extending right from $-1$.