Solve for x: 1170 / (x - 42) = 26
Understand the Problem
The question requires us to solve an equation for the variable 'x'. The equation involves a fraction and requires algebraic manipulation to isolate 'x'. It involves multiplying both sides by (x-42) then isolating the x term.
Answer
$x = 87$
Answer for screen readers
$x = 87$
Steps to Solve
- Multiply both sides by $(x - 42)$
To eliminate the fraction, multiply both sides of the equation by $(x - 42)$:
$$ \frac{1170}{x-42} \cdot (x - 42) = 26 \cdot (x - 42) $$
This simplifies to:
$$ 1170 = 26(x - 42) $$
- Distribute on the right side
Distribute the 26 on the ride side of the equation:
$$ 1170 = 26x - 26 \cdot 42 $$
$$ 1170 = 26x - 1092 $$
- Isolate the term with $x$
Add 1092 to both sides of the equation to isolate the term with $x$:
$$ 1170 + 1092 = 26x - 1092 + 1092 $$
$$ 2262 = 26x $$
- Solve for $x$
Divide both sides by 26 to solve for $x$:
$$ \frac{2262}{26} = \frac{26x}{26} $$
$$ x = 87 $$
$x = 87$
More Information
The solution to the equation $\frac{1170}{x-42} = 26$ is $x = 87$.
Tips
A common mistake is not distributing the $26$ correctly on the right side of the equation in step 2. Another common mistake is making an arithmetic error when adding or dividing.
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