Question

Solve l 3x-7 l = 2

Answer 1

Answer:

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

2) Solution are x ≤ 13/2 and  x ≤ -3/2

Step-by-step explanation:

1) Given absolute inequality,

|3x-7| = 2

⇒ 3x - 7 = ± 2

⇒ 3x = 7 ± 2

$\implies x=\frac{7\pm 2}{3}$

$x=\frac{7+2}{3}\text{ or }x=\frac{7-2}{3}$

$\implies x = 3\text{ or }x=\frac{5}{3}$

2) l 2x-5 l ≤ 8

⇒  2x-5  ≤ ±8

⇒   2x ≤ 5 ± 8

$\implies x\leq \frac{5\pm 8}{2}$

$x\leq \frac{5+8}{2}\text{ or }x\leq \frac{5-8}{2}$

$\implies x \leq \frac{13}{2}\text{ or }x\leq-\frac{3}{2}$

Answer 2

Answer:

Answer:

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

2) Solution are x ≤ 13/2 and  x ≤ -3/2

Step-by-step 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