Answer:
The values of x = [-1.5, -∞) and [9.6, ∞)
Step-by-step explanation:
Here we have to solve the given system of inequalities.
12x + 7 ≤ -11 and 5x - 8 ≥ 40
Here we have to solve for x. Let's take the first inequality and solve for x.
12x + 7 ≤ -11
Subtracting 7 from both sides,
12x + 7 - 7 ≤ -11 - 7
12x ≤ -18
Dividing both sides by 12, we get
x ≤ [tex]\frac{-18}{12}[/tex]
We can simplify this fraction.
x [tex]\leq \frac{-3}{2}[/tex]
x [tex]\leq -1.5[/tex]
Now let's solve the second inequality.
5x - 8 ≥ 40
Add 8 on both sides,
5x - 8 + 8 ≥ 40 + 8
5x ≥ 48
Dividing both sides by 5, we get
x ≥ [tex]\frac{48}{5}[/tex]
x ≥ 9.6
So, solving those inequalities, we get
x ≤ -1.5 and x ≥ 9.6
This means, the values of x = [-1.5, -∞) and [9.6, ∞)
Let's draw the solution in a number line.
