Question

12x+7<-11 AND 5x-8=>40

Answer 1

12x + 7 < -11

12x < -18

x < -1.5

5x - 8 => 40

5x => 48

x => 9.6

Answer 2

The values of x = [-1.5, -∞) and [9.6, ∞)

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 ≤
`(-18)/(12)`

We can simplify this fraction.

x
`\leq (-3)/(2)`

x
`\leq -1.5`

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 ≥
`(48)/(5)`

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.