MATH SOLVE

3 months ago

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

Accepted Solution

A:

Answer:1) Solutions are x = 3 and x = 5/32) Solution are x ≤ 13/2 and x ≤ -3/2Step-by-step explanation:1) Given absolute inequality,|3x-7| = 2⇒ 3x - 7 = ± 2⇒ 3x = 7 ± 2[tex]\implies x=\frac{7\pm 2}{3}[/tex][tex]x=\frac{7+2}{3}\text{ or }x=\frac{7-2}{3}[/tex][tex]\implies x = 3\text{ or }x=\frac{5}{3}[/tex]2) l 2x-5 l ≤ 8⇒ 2x-5 ≤ ±8⇒ 2x ≤ 5 ± 8[tex]\implies x\leq \frac{5\pm 8}{2}[/tex][tex]x\leq \frac{5+8}{2}\text{ or }x\leq \frac{5-8}{2}[/tex][tex]\implies x \leq \frac{13}{2}\text{ or }x\leq-\frac{3}{2}[/tex]