Solve the following linear equation for

Question

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 first simplify both sides.

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: \[ 9 + 10 + 3x = 19 + 3x \]

Now we have the equation: \[ 6x - 2 = 19 + 3x \]

3. Next, isolate \( x \). Start by subtracting \( 3x \) from both sides: \[ 6x - 3x - 2 = 19 \] This simplifies to: \[ 3x - 2 = 19 \]

4. Now, add \( 2 \) to both sides: \[ 3x = 21 \]

5. Finally, divide by \( 3 \): \[ x = 7 \]

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