Question

Which?
Of the following equations has the same solution as the equation x plus one half equals negative one fourth
A. X+1/2=5/4
B. X-1.5=0.75

Answer 1

Let's start by solving the given equation:

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

To isolate \( x \), we can subtract \( \frac{1}{2} \) from both sides:

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

Now, we need to convert \( \frac{1}{2} \) to a fraction with a denominator of 4 for easier subtraction:

\[ \frac{1}{2} = \frac{2}{4} \]

So, we can rewrite the equation as:

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

Combining the fractions gives us:

\[ x = -\frac{3}{4} \]

Now we have found that the solution to the original equation is \( x = -\frac{3}{4} \).

Next, let's check which of the provided options has the same solution:

**Option A:**
\[ x + \frac{1}{2} = \frac{5}{4} \]
Subtract \( \frac{1}{2} \) (or \( \frac{2}{4} \)) from both sides:
\[ x = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} \]
The solution is \( x = \frac{3}{4} \).

**Option B:**
\[ x - 1.5 = 0.75 \]
Add \( 1.5 \) to both sides. Remember that \( 1.5 \) can be written as \( \frac{3}{2} \) or \( \frac{6}{4} \):
\[ x = 0.75 + 1.5 = 0.75 + \frac{6}{4} \]
Convert \( 0.75 \) to a fraction:
\[ 0.75 = \frac{3}{4} \]
Now add the two fractions:
\[ x = \frac{3}{4} + \frac{6}{4} = \frac{9}{4} \]
The solution is \( x = \frac{9}{4} \).

Now, comparing the two results:
- Option A leads to \( x = \frac{3}{4} \).
- Option B leads to \( x = \frac{9}{4} \).

Neither option has the same solution as the original equation \( x + \frac{1}{2} = -\frac{1}{4} \), which solved to \( x = -\frac{3}{4} \). Thus, neither option is correct.