(4) $\\frac{1}{2}x + 3 = \\frac{1}{3}x + 2$\n(7) $\\frac{1}{3}x + \\frac{1}{2} = \\frac{1}{4}x + 1$\n(5)…

(4) $\\frac{1}{2}x + 3 = \\frac{1}{3}x + 2$\n(7) $\\frac{1}{3}x + \\frac{1}{2} = \\frac{1}{4}x + 1$\n(5) $-\\frac{1}{2}x + 3 = \\frac{1}{3}x - 2$\n(8) $\\frac{1}{3}x - \\frac{1}{2} = \\frac{1}{4}x + 1$\n(6) $-\\frac{1}{2}x + 3 = -\\frac{1}{3}x - 2$\n(9) $-\\frac{1}{3}x - \\frac{1}{2} = -\\frac{1}{4}x - 1$\n
Answer
Explanation:
Step1: Move the terms with (x) to one side
For equation (\frac{1}{2}x + 3=\frac{1}{3}x + 2), subtract (\frac{1}{3}x) from both sides: (\frac{1}{2}x-\frac{1}{3}x+3 = 2).
Step2: Calculate the coefficient of (x)
(\frac{1}{2}x-\frac{1}{3}x=\frac{3x - 2x}{6}=\frac{1}{6}x), so the equation becomes (\frac{1}{6}x+3 = 2).
Step3: Move the constant term
Subtract 3 from both sides: (\frac{1}{6}x=2 - 3=-1).
Step4: Solve for (x)
Multiply both sides by 6: (x=-6).
Answer:
(x = - 6)