Question

-11 + 10(p + 10) =4 - 5(2p + 11)

Answer 1

To solve the equation \(-11 + 10(p + 10) = 4 - 5(2p + 11)\), we will start by simplifying both sides step-by-step.

**Step 1: Expand both sides.**

On the left side:

\[
-11 + 10(p + 10) = -11 + 10p + 100 = 10p + 89
\]

On the right side:

\[
4 - 5(2p + 11) = 4 - 10p - 55 = -10p - 51
\]

So the equation now looks like this:

\[
10p + 89 = -10p - 51
\]

**Step 2: Combine like terms.**

Add \(10p\) to both sides:

\[
10p + 10p + 89 = -51
\]

This simplifies to:

\[
20p + 89 = -51
\]

**Step 3: Isolate the \(p\) term.**

Subtract \(89\) from both sides:

\[
20p = -51 - 89
\]

Simplifying that gives:

\[
20p = -140
\]

**Step 4: Solve for \(p\).**

Now divide both sides by \(20\):

\[
p = \frac{-140}{20} = -7
\]

Thus, the solution is:

\[
\boxed{-7}
\]