Question

carlos is solving the equation 1/4x-5/2=-1/8 he gets 21/2 what did he do wrong

Answer 1

carolos steps:add 5/2 to both sides, -1/8+5/2=-1/8+20/8=21/8/mutiply both sides by 4, 4*21/8=21/2

what he do wrong

Answer 2

Let's solve the equation step by step and see where Carlos might have made a mistake.

The equation given is:

\[
\frac{1}{4}x - \frac{5}{2} = -\frac{1}{8}
\]

1. **Add \(\frac{5}{2}\) to both sides**:
\[
\frac{1}{4}x = -\frac{1}{8} + \frac{5}{2}
\]

To add the fractions on the right, we need a common denominator. The common denominator between 8 and 2 is 8. Convert \(\frac{5}{2}\) to eighths:

\[
\frac{5}{2} = \frac{20}{8}
\]

Now substitute this back into the equation:

\[
\frac{1}{4}x = -\frac{1}{8} + \frac{20}{8} = \frac{19}{8}
\]

2. **Multiply both sides by 4 to isolate \(x\)**:
\[
x = 4 \cdot \frac{19}{8}
\]

To multiply, we can simplify:
\[
x = \frac{76}{8} = \frac{19}{2}
\]

So the correct solution for \(x\) is \(\frac{19}{2}\).

If Carlos got \(\frac{21}{2}\), he might have made a calculation error in either the addition of fractions or the multiplication step. Specifically, the error likely happened when he was adding \(-\frac{1}{8}\) and \(\frac{5}{2}\). Always ensure to convert to a common denominator correctly and to double-check calculations during each step.

Answer 3

Let’s clarify Carlos's steps and identify the error:

1. **Starting equation:**
\[
\frac{1}{4}x - \frac{5}{2} = -\frac{1}{8}
\]

2. **Add \(\frac{5}{2}\) to both sides:**
\[
\frac{1}{4}x = -\frac{1}{8} + \frac{5}{2}
\]

3. **Carlos's step:**
- He writes \(-\frac{1}{8} + \frac{5}{2} = -\frac{1}{8} + \frac{20}{8} = \frac{21}{8}\).

Here’s the error:
- When adding \(-\frac{1}{8}\) and \(\frac{20}{8}\), the correct calculation should be:
\[
-\frac{1}{8} + \frac{20}{8} = \frac{19}{8}
\]

Carlos incorrectly calculated \( -\frac{1}{8} + \frac{20}{8} \) as \( \frac{21}{8} \).

4. **Multiply both sides by 4:**
\[
x = 4 \cdot \frac{21}{8} = \frac{84}{8} = \frac{21}{2}
\]

Since he arrived at \(\frac{21}{2}\) because of the earlier mistake in the fraction addition, the correct answer should have been based on \(\frac{19}{8}\) instead.

If he had correctly calculated the addition of fractions, he would have subsequently multiplied:
\[
x = 4 \cdot \frac{19}{8} = \frac{76}{8} = \frac{19}{2}.
\]

So, the entire problem arose from incorrectly calculating \(-\frac{1}{8} + \frac{5}{2}\).