To solve the equation 3x + 2x + 5 = 4x + 2, we will follow these steps:
- Combine like terms on the left side:
The left side of the equation can be simplified by combining the terms with x.
So, 3x + 2x becomes 5x. Thus, the equation now looks like this:
5x + 5 = 4x + 2
- Isolate the variable:
Next, we want to get all terms involving x on one side of the equation and constant terms on the other side. To do this, we can subtract 4x from both sides:
5x - 4x + 5 = 4x - 4x + 2
This simplifies to:
x + 5 = 2
- Subtract the constant:
Now, we’ll isolate x completely by getting rid of the 5 on the left. Subtract 5 from both sides:
x + 5 - 5 = 2 - 5
This gives us:
x = -3
So, the solution to the equation 3x + 2x + 5 = 4x + 2 is x = -3.
It’s always a good idea to double-check your solution by substituting -3 back into the original equation:
3(-3) + 2(-3) + 5 ?= 4(-3) + 2
Calculating each side:
-9 - 6 + 5 ?= -12 + 2
-10 ?= -10
Both sides are equal, confirming that our solution is correct!