Solving the Equation: 1/11+x=-3 1/2
Understanding the Equation
The given equation is a linear equation in the form of:
1/11 + x = -3 1/2
To solve for x, we need to isolate the variable x on one side of the equation.
Simplifying the Right-Hand Side
The right-hand side of the equation is a mixed number, which can be simplified to an improper fraction.
-3 1/2 = (-3 × 2 + 1) / 2 = -7 / 2
So, the equation becomes:
1/11 + x = -7/2
Isolating x
To isolate x, we can subtract 1/11 from both sides of the equation.
x = -7/2 - 1/11
Combining Fractions
To combine the fractions on the right-hand side, we need to find the least common multiple (LCM) of 2 and 11, which is 22. Then, we can convert both fractions to have a denominator of 22.
x = (-7 × 11)/22 - (1 × 2)/22 x = -77/22 - 2/22 x = (-77 - 2)/22 x = -79/22
Simplifying the Answer
The final answer is:
x = -79/22
Conclusion
By solving the equation 1/11 + x = -3 1/2, we found that the value of x is -79/22.
