Answer:
Part A: x = -24
Part B: n = 2
Step-by-step explanation:
Part A:
The algebraic expression for: "StartFraction 2 Over 3 EndFraction left-parenthesis StartFraction one-half EndFraction. x plus 12 right-parenthesis equals left-parenthesis StartFraction one-half EndFraction left-parenthesis StartFraction one-third EndFraction x plus 14 right-parenthesis minus 3" will be ⇒ [tex]\frac{2}{3} (\frac{1}{2} x+12)=(\frac{1}{2} (\frac{1}{3} x+14)-3)[/tex]
Multiply both sides by 6
∴ [tex]6 * \frac{2}{3} (\frac{1}{2} x+12)=6*(\frac{1}{2} (\frac{1}{3} x+14)-3)[/tex]
∴[tex]4*(\frac{1}{2} x+12)=3 (\frac{1}{3} x+14)-18[/tex]
∴ 2x + 4*12 = x + 3 *14 - 18
∴ 2x - x = 3 * 14 - 18 - 4 * 12 = -24
∴ x = -24
============================================================
Part B:
The algebric expression for: "StartFraction one-half EndFraction left-parenthesis n minus 4 right-parenthesis minus 3 equals 3 minus left-parenthesis 2 n plus 3 right-parenthesis" will be ⇒ [tex]\frac{1}{2}(n-4)-3=3-(2n+3)[/tex]
Multiply both sides by 2
(n-4) - 6 = 6 - 2(2n+3)
n - 4 - 6 = 6 - 4n - 6
Combine like terms
n + 4 n = 4 + 6
5n = 10
n = 10/5 = 2
∴ n = 2
