Question

What is the value of x in the equation ?

Answer 1

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 ⇒ $\frac{2}{3} (\frac{1}{2} x+12)=(\frac{1}{2} (\frac{1}{3} x+14)-3)$

Multiply both sides by 6

∴ $6 * \frac{2}{3} (\frac{1}{2} x+12)=6*(\frac{1}{2} (\frac{1}{3} x+14)-3)$

∴$4*(\frac{1}{2} x+12)=3 (\frac{1}{3} x+14)-18$

∴ 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 ⇒ $\frac{1}{2}(n-4)-3=3-(2n+3)$

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

Answer 2

Answer:

the answer is n=2

Step-by-step explanation: