Question

Solve the following linear equation for
x
x.

​

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

​

​​
x
=
x=

Answer 1

To solve the equation \( 5x - 2 + x = 9 + 3x + 10 \), we start by simplifying both sides of the equation.

1. Combine like terms on the left side:
\[
5x + x - 2 = 6x - 2
\]
So the left side becomes \( 6x - 2 \).

2. Combine like terms on the right side:
\[
9 + 10 + 3x = 19 + 3x
\]
So the right side becomes \( 19 + 3x \).

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

3. Now, we can isolate the variable \( x \). First, let's subtract \( 3x \) from both sides:
\[
6x - 3x - 2 = 19
\]
Which simplifies to:
\[
3x - 2 = 19
\]

4. Next, add \( 2 \) to both sides:
\[
3x = 19 + 2
\]
Which simplifies to:
\[
3x = 21
\]

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

Therefore, the solution is:
\[
x = 7
\]