Final Answer: [tex]x = 12[/tex]
Steps/Reasons/Explanation:
Question: What is the solution to the equation [tex]\frac{1}{2}x + 3 = \frac{2}{3}x + 1?[/tex]
Step 1: Simplify [tex]\frac{1}{2}x[/tex] to [tex]\frac{x}{2}[/tex].
[tex]\frac{x}{2} + 3 = \frac{2}{3}x + 1[/tex]
Step 2: Simplify [tex]\frac{2}{3}x[/tex] to [tex]\frac{2x}{3}[/tex].
[tex]\frac{x}{2} + 3 = \frac{2x}{3} + 1[/tex]
Step 3: Multiply both sides by [tex]6[/tex] (LCM of [tex]2, 3[/tex]).
[tex]3x + 18 = 4x + 6[/tex]
Step 4: Subtract [tex]3x[/tex] from both sides.
[tex]18 = 4x + 6 - 3x[/tex]
Step 5: Simplify [tex]4x + 6 - 3x[/tex] to [tex]x + 6[/tex].
[tex]18 = x + 6[/tex]
Step 6: Subtract [tex]6[/tex] from both sides.
[tex]18 - 6 = x[/tex]
Step 7: Simplify [tex]18 - 6[/tex] to [tex]12[/tex].
[tex]12 = x[/tex]
Step 8: Switch sides.
[tex]x = 12[/tex]
~I hope I helped you :)~
