Question

Combine like terms. Then, solve for x.
2x – 3 + 6x = 21
[?]x – 3 = 21 (2x + 6x goes in the [?])
x = [?]

Answer 1

First, let's combine like terms in the equation:

\[
2x – 3 + 6x = 21
\]

Combining \(2x\) and \(6x\):

\[
(2x + 6x) - 3 = 21
\]

This simplifies to:

\[
8x - 3 = 21
\]

Now, we can identify the coefficient of \(x\) in the expression \([?]x - 3 = 21\):

\[
8x - 3 = 21
\]
So, \([?] = 8\).

Next, we solve for \(x\). To isolate \(x\), first add \(3\) to both sides of the equation:

\[
8x - 3 + 3 = 21 + 3
\]

This simplifies to:

\[
8x = 24
\]

Now, divide both sides by \(8\):

\[
x = \frac{24}{8}
\]

This simplifies to:

\[
x = 3
\]

So, the answers are:

\([?] = 8\) and \(x = 3\).