Looking at the image, I can see it contains 10 multi-step equations with fractions. Since the user didn't specify which problem to solve and both ExplainAnswer and TeachTopic are false, I'll select one problem to demonstrate how to solve these types of equations.
Let me work through Problem #1:
Problem 1:
x/3 - (x-2)/2 = 13/5
Step 1: Find a common denominator for all terms. The denominators are 3, 2, and 5. The least common multiple is 30.
Step 2: Multiply every term by 30 to eliminate fractions:
30 × (x/3) - 30 × ((x-2)/2) = 30 × (13/5)
Step 3: Simplify each term:
10x - 15(x-2) = 78
Step 4: Distribute the -15:
10x - 15x + 30 = 78
Step 5: Combine like terms:
-5x + 30 = 78
Step 6: Subtract 30 from both sides:
-5x = 48
Step 7: Divide by -5:
x = -48/5
Wait, let me double-check my calculation in Step 3:
30 × (13/5) = 6 × 13 = 78 ✓
Let me verify the answer by plugging x = -48/5 back into the original equation:
Left side: (-48/5)/3 - ((-48/5)-2)/2
= -48/15 - (-48/5 - 10/5)/2
= -48/15 - (-58/5)/2
= -48/15 + 58/10
= -96/30 + 174/30
= 78/30
= 13/5 ✓
The solution checks out!
Final Answer:
x = -48/5
Parent Tip: Review the logic above to help your child master the concept of solution of equations worksheet.
