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Answer
The solutions are \( x = 66 \) and \( x = -44 \).
Solution
We begin with the equation
|x/11 – 1| = 5.
The definition of absolute value tells us that if |A| = B (with B ≥ 0), then A = B or A = –B. Applying that here gives us two equations:
1) x/11 – 1 = 5
2) x/11 – 1 = –5
Now, solve each equation separately.
For the first equation:
x/11 – 1 = 5
Add 1 to both sides:
x/11 = 6
Multiply both sides by 11:
x = 66
For the second equation:
x/11 – 1 = –5
Add 1 to both sides:
x/11 = –4
Multiply both sides by 11:
x = –44
Thus, the solutions to the equation are x = 66 and x = –44.
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Simplify this solution Mind Expander
To solve the equation \( 5 = \left| \frac{x}{11} - 1 \right| \), we need to consider the definition of absolute value, which leads to two possible equations: 1. \( \frac{x}{11} - 1 = 5 \) 2. \( \frac{x}{11} - 1 = -5 \) Solving the first equation: \[ \frac{x}{11} - 1 = 5 \implies \frac{x}{11} = 6 \implies x = 66 \] Now for the second equation: \[ \frac{x}{11} - 1 = -5 \implies \frac{x}{11} = -4 \implies x = -44 \] Thus, the solutions for the equation \( 5 = \left| \frac{x}{11} - 1 \right| \) are \( x = 66 \) and \( x = -44 \).
