Solve $\frac{x-1}{11}=-2$ for $x$.
Answer (2)
Multiply both sides of the equation by 11: x − 1 = − 22 .
Add 1 to both sides of the equation: x = − 22 + 1 .
Simplify to find the value of x : x = − 21 .
The solution to the equation is − 21 .
Explanation
Problem Analysis We are given the equation 11 x − 1 = − 2 and we need to solve for x .
Multiply both sides by 11 To isolate x − 1 , we multiply both sides of the equation by 11: 11 x − 1 × 11 = − 2 × 11 x − 1 = − 22
Add 1 to both sides To solve for x , we add 1 to both sides of the equation: x − 1 + 1 = − 22 + 1 x = − 21
Final Answer Therefore, the solution is x = − 21 .
Examples
In real-world scenarios, solving linear equations like this can help determine unknown quantities. For example, if you know that a certain discount, represented by 11 x − 1 , results in a final price of -2 dollars, you can solve for the original price x . This type of problem-solving is useful in finance, engineering, and everyday problem-solving where you need to find an unknown value based on a given relationship.
To solve 11 x − 1 = − 2 , first multiply both sides by 11 to eliminate the fraction, resulting in x − 1 = − 22 . Then add 1 to both sides to isolate x , yielding the solution x = − 21 . Thus, the final answer is x = − 21 .
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