Question

ustify your steps using the properties of equality and determine the number of solutions to the equation 32(4−8x)+5x=1−7x
.(4 points)make it easy and east to copy down...make it in at least 6 sentences

Answer 1

To solve the equation \( 32(4 - 8x) + 5x = 1 - 7x \), we first distribute the \( 32 \) on the left side. Using the distributive property, we have:

\[
32 \cdot 4 - 32 \cdot 8x = 128 - 256x.
\]

Now the equation becomes:

\[
128 - 256x + 5x = 1 - 7x.
\]

Next, we combine like terms on the left side. Combining \(-256x\) and \(5x\) gives:

\[
128 - 251x = 1 - 7x.
\]

Then, we can add \(7x\) to both sides to eliminate the \(7x\) from the right side:

\[
128 - 251x + 7x = 1.
\]

This simplifies to:

\[
128 - 244x = 1.
\]

To isolate \(x\), we first subtract \(128\) from both sides:

\[
-244x = 1 - 128,
\]

which simplifies to:

\[
-244x = -127.
\]

Now, divide both sides by \(-244\):

\[
x = \frac{-127}{-244} = \frac{127}{244}.
\]

Since we obtained a unique value for \(x\), there is exactly **one solution** to the equation \( 32(4 - 8x) + 5x = 1 - 7x \).