Question

Solve the following system of linear inequalities. 3x − 9 ≥ 0, 4x − 10 ≤ 6.
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Answer 1

Answer:

−4≤x≤1

Step-by-step explanation:

(x+5)−7(x−2)≥4x+9

⇒x+5−7x+14≥4x+9

⇒−6x+19≥4x+9

Add −4x and −19 both sides, we get

−6x+19−4x−19≥4x+9−4x−19

⇒−6x−4x≥9−19

⇒−10x≥−10

Divided by −10, we get

x≤1

Also,

2(x−3)−7(x+5)≤3x−9

⇒2x−6−7x−35≤3x−9

⇒−5x−41≤3x−9

Add −3x and −41 both sides, we get

−5x−41−3x+41≤3x−9−3x+41

⇒−5x−3x≤−9+41

⇒−8x≤32

Divided by −8 both sides, we get

x≥−4

Then −4≤x≤1

Answer 2

Answer:

Solve the following system of linear inequalities. 3x − 9 ≥ 0, 4x − 10 ≤ 6.