Question

Solve l 3x-7 l = 2

and solve l 2x-5 l< or equal to 8
the lines (l) signifies absolute values therefore l 3x-7 l is the absolute value of that and same thing for 2x-5

Answer 1

Answer:

1) Solutions are x = 3 and x = 5/3

2) Solution are x ≤ 13/2 and x ≤ -3/2

Explanation:

1) Given absolute inequality,

|3x-7| = 2

⇒ 3x - 7 = ± 2

⇒ 3x = 7 ± 2

2) l 2x-5 l ≤ 8

⇒ 2x-5 ≤ ±8

⇒ 2x ≤ 5 ± 8

Answer 2

1) Solutions are x = 3 and x = 5/3

2) Solution are x ≤ 13/2 and x ≤ -3/2

Explanation:

1) Given absolute inequality,

|3x-7| = 2

⇒ 3x - 7 = ± 2

⇒ 3x = 7 ± 2

`\implies x=(7\pm 2)/(3)`

`x=(7+2)/(3)\text{ or }x=(7-2)/(3)`

`\implies x = 3\text{ or }x=(5)/(3)`

2) l 2x-5 l ≤ 8

⇒ 2x-5 ≤ ±8

⇒ 2x ≤ 5 ± 8

`\implies x\leq (5\pm 8)/(2)`

`x\leq (5+8)/(2)\text{ or }x\leq (5-8)/(2)`

`\implies x \leq (13)/(2)\text{ or }x\leq-(3)/(2)`