Question

solve it!!!!!!!!!!!!!!!!!!!!!! FAST!!!!!!

Answer 1

QUESTION:

Solve the inequalities

• 2 ≤ 3x - 4 ≤ 5
• - 3 ≤ 4 - 7x/2 ≤ 18
• - 15 ≤ 3(x - 2)/5 ≤ 0

ANSWER:

• (i) x lies between the interval [2 , 3]
• (ii) x lies between the interval [- 4 , 2]
• (iii)x lies between the interval [- 23,2]

TO FIND:

• The values of x.

EXPLANATION:

1) 2 ≤ 3x - 4 ≤ 5

3x - 4 ≥ 2

3x ≥ 2 + 4

3x ≥ 6

x ≥ 2

3x ≤ 5 + 4

3x ≤ 9

x ≤ 3

2 ≤ x ≤ 3

x lies between the interval [2 , 3]

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2) - 3 ≤ 4 - 7x/2 ≤ 18

4 - 7x/2 ≥ - 3

- 7x/2 ≥ - 3 - 4

- 7x /2 ≥ - 7

Multiply by minus sign. So the symbol is also reversed.

7x/2 ≤ 7

x/2 ≤ 1

x ≤ 2

4 - 7x/2 ≤ 18

- 7x/2 ≤ 14

Multiply by minus sign. So the symbol is also reversed.

7x/2 ≥ - 14

x/2 ≥ - 2

x ≥ - 4

2 ≤ x ≤ - 4

x lies between the interval [- 4 , 2]

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3) - 15 ≤ 3(x - 2)/5 ≤ 0

- 15 ≤ 3(x - 2)/5

- 5 ≤ (x - 2)/5

- 25 ≤ x - 2

x ≥ - 23

3(x - 2)/5 ≤ 0

(x - 2)/5 ≤ 0

x - 2 ≤ 0

x ≤ 2

- 23 ≥ x ≥ 2

x lies between the interval [- 23, 2]