How do I solve 8j - 5 + j = 67?
Understand the Problem
The question is asking how to solve the algebraic equation 8j - 5 + j = 67. To solve for j, we will combine like terms and isolate j on one side of the equation.
Answer
$j = 8$
Answer for screen readers
The final answer is $j = 8$.
Steps to Solve
- Combine Like Terms
First, we combine the like terms on the left side of the equation. The equation is:
$$8j - 5 + j = 67$$
The like terms, $8j$ and $j$, can be added together:
$$ (8j + j) - 5 = 67 $$
This simplifies to:
$$ 9j - 5 = 67 $$
- Isolate the Variable j
Next, we want to isolate $j$ by adding 5 to both sides of the equation to eliminate the constant:
$$ 9j - 5 + 5 = 67 + 5 $$
This simplifies to:
$$ 9j = 72 $$
- Solve for j
Now, we divide both sides by 9 to solve for $j$:
$$ j = \frac{72}{9} $$
This simplifies to:
$$ j = 8 $$
The final answer is $j = 8$.
More Information
The solution indicates that when $j$ equals 8, the original equation holds true. You can check this by substituting $j$ back into the original equation:
$$ 8(8) - 5 + 8 = 67 $$
This gives:
$$ 64 - 5 + 8 = 67 $$
So, $67 = 67$, verifying our solution is correct!
Tips
- Miscombining Terms: Sometimes students forget to correctly combine coefficients when adding like terms. Always ensure to recheck your combining steps.
- Not Isolating the Variable: Some may forget to properly isolate the variable by not performing the same operation on both sides of the equation.
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