Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Solve for x.
1/5(x + 0.5) + 5.24 = 3/2 x + 7/10(x + 2.2)

The value of x is
Answer
pick one
Answer
no
Answered by GPT-4o mini
To solve for \( x \) in the equation

\[
\frac{1}{5}(x + 0.5) + 5.24 = \frac{3}{2} x + \frac{7}{10}(x + 2.2),
\]

we will simplify and combine like terms step-by-step.

1. Start with the left side:
\[
\frac{1}{5}(x + 0.5) + 5.24 = \frac{1}{5}x + \frac{1}{10} + 5.24.
\]
We convert \( 5.24 \) into a fraction:
\[
5.24 = \frac{524}{100} = \frac{131}{25}.
\]
So,
\[
\frac{1}{5}(x + 0.5) + 5.24 = \frac{1}{5}x + \frac{1}{10} + \frac{131}{25}.
\]
Finding a common denominator (which is 50):
\[
\frac{1}{10} = \frac{5}{50}, \quad \frac{131}{25} = \frac{262}{50}.
\]
Thus,
\[
\frac{1}{5}x + \frac{1}{10} + \frac{131}{25} = \frac{1}{5}x + \frac{5}{50} + \frac{262}{50} = \frac{1}{5}x + \frac{267}{50}.
\]

2. Now simplify the right side:
\[
\frac{7}{10}(x + 2.2) = \frac{7}{10}x + \frac{7 \cdot 2.2}{10} = \frac{7}{10}x + \frac{15.4}{10} = \frac{7}{10}x + \frac{77}{100}.
\]
We need a common denominator of 100:
\[
\frac{3}{2}x = \frac{150}{100}x, \quad \frac{7}{10}x = \frac{70}{100}x.
\]
Therefore:
\[
\frac{3}{2} x + \frac{7}{10}(x + 2.2) = \frac{150}{100}x + \frac{70}{100}x + \frac{77}{100} = \frac{220}{100}x + \frac{77}{100}.
\]

3. Now we have:
\[
\frac{1}{5}x + \frac{267}{50} = \frac{220}{100}x + \frac{77}{100}.
\]

4. Next, we'll convert everything to have a common denominator of 100:
\[
\frac{1}{5}x = \frac{20}{100}x, \quad \frac{267}{50} = \frac{534}{100}.
\]
Thus the left side simplifies to:
\[
\frac{20}{100}x + \frac{534}{100}.
\]

5. Equating both sides:
\[
\frac{20}{100}x + \frac{534}{100} = \frac{220}{100}x + \frac{77}{100}.
\]
To simplify:
\[
\frac{534 - 77}{100} = \frac{220 - 20}{100}x \implies \frac{457}{100} = \frac{200}{100}x \implies 457 = 200x.
\]
We can isolate \( x \):
\[
x = \frac{457}{200}.
\]

So the value of \( x \) is

\[
\frac{457}{200}.
\]

To express it more simply, we can write it as 2.285. Hence, in the specified format:

The value of x is \( 2.285 \) or \( \frac{457}{200} \).

Using the final answer in the asked format would give:

The value of x is \( 2.285 \).
Answered by GPT-4o mini
The value of \( x \) is \( 2.285 \).
Answered by GPT-4o mini
I apologize for any confusion. The correct answer formatted as requested is:

The value of \( x \) is \( \frac{457}{200} \).