Chapter2: Solving Linear Equations
Section2.4: Solve Mixture And Uniform Motion Applications
Problem 2.90TI: Thanh and Nhat leave their office in Sacramento at the same time. Thanh drives north on I-5 at a...
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![**Solving Linear Equations: Example Problem**
In this example, we will solve the following linear equation for \( x \):
\[ \frac{5}{8}x + \frac{1}{16}x = \frac{11}{16} + x \]
**Step-by-Step Solution:**
1. **Simplify and Combine Like Terms:**
- To solve the equation, we first need to combine the terms involving \( x \) on the left side.
Combine \(\frac{5}{8}x\) and \(\frac{1}{16}x\):
Notice that in order to combine these, they need a common denominator.
\[\frac{5}{8}x = \frac{10}{16}x\]
Now, the equation becomes:
\[\frac{10}{16}x + \frac{1}{16}x = \frac{11}{16} + x\]
Combine the \(x\) terms on the left side:
\[\frac{11}{16}x = \frac{11}{16} + x\]
2. **Isolate the Variable:**
- Next, we need to isolate \(x\). Start by subtracting \(\frac{11}{16}x\) from both sides of the equation to leave only \(x\) on the right side:
\[\frac{11}{16}x - \frac{11}{16}x = \frac{11}{16} + x - \frac{11}{16}x\]
Simplifying this, we get:
\[ 0 = \frac{11}{16} + \left(1 - \frac{11}{16}\right)x\]
Note that \(1 = \frac{16}{16}\), so the equation becomes:
\[0 = \frac{11}{16} + \left(\frac{16}{16} - \frac{11}{16}\right)x\]
Simplifying further:
\[0 = \frac{11}{16} + \frac{5}{16}x\]
3. **Solving for \(x\):**
- Move \(\frac{11}{16}\) to the other side of the equation by subtracting \(\frac{11}{16}\) from both sides:
\[\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c1b1525-9f55-427c-9418-433680b9f4b9%2F3e694400-b4b1-4b50-b984-59981e5d312f%2Fozdsqrl_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving Linear Equations: Example Problem**
In this example, we will solve the following linear equation for \( x \):
\[ \frac{5}{8}x + \frac{1}{16}x = \frac{11}{16} + x \]
**Step-by-Step Solution:**
1. **Simplify and Combine Like Terms:**
- To solve the equation, we first need to combine the terms involving \( x \) on the left side.
Combine \(\frac{5}{8}x\) and \(\frac{1}{16}x\):
Notice that in order to combine these, they need a common denominator.
\[\frac{5}{8}x = \frac{10}{16}x\]
Now, the equation becomes:
\[\frac{10}{16}x + \frac{1}{16}x = \frac{11}{16} + x\]
Combine the \(x\) terms on the left side:
\[\frac{11}{16}x = \frac{11}{16} + x\]
2. **Isolate the Variable:**
- Next, we need to isolate \(x\). Start by subtracting \(\frac{11}{16}x\) from both sides of the equation to leave only \(x\) on the right side:
\[\frac{11}{16}x - \frac{11}{16}x = \frac{11}{16} + x - \frac{11}{16}x\]
Simplifying this, we get:
\[ 0 = \frac{11}{16} + \left(1 - \frac{11}{16}\right)x\]
Note that \(1 = \frac{16}{16}\), so the equation becomes:
\[0 = \frac{11}{16} + \left(\frac{16}{16} - \frac{11}{16}\right)x\]
Simplifying further:
\[0 = \frac{11}{16} + \frac{5}{16}x\]
3. **Solving for \(x\):**
- Move \(\frac{11}{16}\) to the other side of the equation by subtracting \(\frac{11}{16}\) from both sides:
\[\
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