Final answer:
To solve equation a, simplify both sides of the equation, isolate the variable, and solve for x. The solution is x = 3. To solve equation b, simplify both sides of the equation, combine like terms, isolate the variable, and solve for x. The solution is x = -1.
Step-by-step explanation:
To solve equation a:
We start by simplifying both sides of the equation:
2x + 3 - (x - 1) = 2x - 2 - (-x)
2x + 3 - x + 1 = 2x - 2 + x
x + 4 = 3x - 2
We then subtract x from both sides to isolate the variable:
4 = 2x - 2
Next, we add 2 to both sides of the equation:
4 + 2 = 2x - 2 + 2
6 = 2x
Finally, we divide both sides by 2 to solve for x:
6/2 = 2x/2
x = 3
Therefore, the solution to equation a is x = 3.
To solve equation b:
We start by simplifying both sides of the equation:
2x - (x - 2) = -2 - (x - 1)
2x - x + 2 = -2 - x + 1
x + 2 = -1 - x + 1
We then combine like terms:
x + 2 = -x
Next, we subtract x from both sides of the equation:
x - x + 2 = -x - x
2 = -2x
Finally, we divide both sides by -2 to solve for x:
2/-2 = -2x/-2
-1 = x
Therefore, the solution to equation b is x = -1.