Question

1
Solve the following linear equation for
x
x.

​

5
x
−
2
+
x
=
9
+
3
x
+
10
5x−2+x=9+3x+10

​

Answer 1

To solve the equation \( 5x - 2 + x = 9 + 3x + 10 \), let's first simplify both sides.

Combine like terms on both sides:

1. On the left side:
\[
5x + x - 2 = 6x - 2
\]

2. On the right side:
\[
9 + 10 + 3x = 19 + 3x
\]

Now the equation looks like this:
\[
6x - 2 = 19 + 3x
\]

Next, we will isolate \( x \) by moving all \( x \) terms to one side and constant terms to the other side. First, subtract \( 3x \) from both sides:
\[
6x - 3x - 2 = 19
\]
This simplifies to:
\[
3x - 2 = 19
\]

Now, add \( 2 \) to both sides:
\[
3x = 19 + 2
\]
Simplifying this gives:
\[
3x = 21
\]

Finally, divide both sides by \( 3 \):
\[
x = \frac{21}{3} = 7
\]

So the solution is:
\[
\boxed{7}
\]