Matthews King
09/28/2024 · Elementary School
(14) \( \frac{1}{3} x=x+8 \) \( \frac{1}{3} x+1 \) to solve
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Step-by-step Solution
Solve the equation \( \frac{1}{3}x=x+8 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{1}{3}x=x+8\)
- step1: Move the variable to the left side:
\(\frac{1}{3}x-x=8\)
- step2: Subtract the terms:
\(-\frac{2}{3}x=8\)
- step3: Change the signs:
\(\frac{2}{3}x=-8\)
- step4: Multiply by the reciprocal:
\(\frac{2}{3}x\times \frac{3}{2}=-8\times \frac{3}{2}\)
- step5: Multiply:
\(x=-12\)
The solution to the equation \( \frac{1}{3}x=x+8 \) is \( x=-12 \).
Now, we need to solve the expression \( \frac{1}{3}x+1 \) using the value of \( x=-12 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(\frac{1}{3}x+1\)
- step1: Substitute:
\(\frac{1}{3}\left(-12\right)+1\)
- step2: Multiply the numbers:
\(-4+1\)
- step3: Add the numbers:
\(-3\)
Substitute \( x=-12 \) into the expression \( \frac{1}{3}x+1 \), we get \( -3 \).
Therefore, the value of the expression \( \frac{1}{3}x+1 \) when \( x=-12 \) is \( -3 \).
Quick Answer
The value of \( \frac{1}{3}x+1 \) when \( x=-12 \) is \( -3 \).
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