Certainly! Let's solve this step-by-step.
1. Understand the problem: We have two rational numbers. Their sum is given as -5, and one of the numbers is [tex]\(\frac{-11}{6}\)[/tex]. We need to find the other number.
2. Set up the equation: Let's denote the unknown rational number by [tex]\( x \)[/tex]. According to the problem, the sum of the two numbers is:
[tex]\[
x + \frac{-11}{6} = -5
\][/tex]
3. Isolate [tex]\( x \)[/tex]: To find [tex]\( x \)[/tex], we need to isolate it on one side of the equation. To do this, subtract [tex]\(\frac{-11}{6}\)[/tex] from both sides of the equation:
[tex]\[
x = -5 - \frac{-11}{6}
\][/tex]
4. Simplify the right-hand side: We need to perform the subtraction:
- First, recognize that subtracting a negative number is the same as adding its positive:
[tex]\[
x = -5 + \frac{11}{6}
\][/tex]
- Next, we need to combine these two terms into a single fraction. To do this, we need a common denominator. The common denominator for these terms is 6.
- Convert -5 to a fraction with a denominator of 6:
[tex]\[
-5 = \frac{-30}{6}
\][/tex]
- Now, add the fractions:
[tex]\[
x = \frac{-30}{6} + \frac{11}{6}
\][/tex]
- Combine the numerators over the common denominator:
[tex]\[
x = \frac{-30 + 11}{6} = \frac{-19}{6}
\][/tex]
5. Interpret the result: The other rational number is:
[tex]\[
x = \frac{-19}{6}
\][/tex]
Thus, the other rational number that sums up with [tex]\(\frac{-11}{6}\)[/tex] to get -5 is [tex]\(\frac{-19}{6}\)[/tex].
Let's review our intermediate results:
- The sum of the two rational numbers is indeed -5.
- One of the numbers is [tex]\(\frac{-11}{6}\)[/tex].
- The other number is [tex]\(\frac{-19}{6}\)[/tex].
These numbers satisfy the given condition perfectly.
