x + 4x = 66 â 5x = 66 â x = 13,2 - go-checkin.com
Solving the Algebra Equation: x + 4x = 66 − 5x = 66 − x = 13 | Step-by-Step Guide
Solving the Algebra Equation: x + 4x = 66 − 5x = 66 − x = 13 | Step-by-Step Guide
When faced with a math challenge like x + 4x = 66 − 5x = 66 − x = 13, clear reasoning and step-by-step breakdowns make all the difference. Whether you're a student tackling algebra for the first time or a parent helping your child understand equations, breaking down such problems helps build confidence and understanding.
Understanding the Equation
Understanding the Context
The equation presented appears in two parts:
- Left side: x + 4x = 66
- Right side: 66 − 5x = 66 − x = 13
Let’s simplify and solve step by step.
Key Insights
Step 1: Simplify the Left Side
Start with the left expression:
x + 4x
Combine like terms:
x + 4x = 5x
So now the equation becomes:
5x = 66 − 5x = 66 − x = 13
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Step 2: Focus on One Side — Right Side
From 66 − 5x = 66 − x = 13, notice patterns:
The phrase 66 − 5x = 66 − x suggests a way to simplify. Subtract 66 from both sides:
66 − 5x − 66 = 66 − x − 66
−5x = −x
Now divide both sides by −1:
5x = x
But this contradicts the original equation unless x = 0 — but that doesn’t satisfy 66 − x = 13, so we must interpret the equation more carefully.
Let’s simplify from 66 − 5x = 66 − x directly:
Subtract 66 from both sides:
−5x = −x
→ −5x + x = 0
→ −4x = 0
→ x = 0, again inconsistent with 66 − x = 13
So our assumption that the full expression 66 − 5x = 66 − x equals the same value may not hold unless equated properly.
