To solve a linear equation in one variable, simplify the equation. To do this, you may have to use the Distributive Property and combine like terms. Then isolate the variable on one side of the equation and solve for the variable.
Solve:
4(x + 2) - 2x = 4x - 2
First apply the Distributive Property
4*x + 4*2 - 2x = 4x - 2
Next, combine like terms (only on the same side of the equal sign).
4x + 8 - 2x = 4x - 2 <------- 4x and -2x are like terms on the left side of the equal sign
2x + 8 = 4x - 2
From here, apply properties of equality so the variable is only on one side of the equation.
2x + 8 = 4x - 2 <-------- Subtract 2x from both sides to remove the variable from the left side
8 = 2x - 2
Now there is a two-step equation.
8 = 2x - 2 <--------- Add two to both sides
10 = 2x <------------Divide both sides by two
5 = x
Lastly, always check your solution by substituting your solution into the original equation.
4(x + 2) - 2x = 4x - 2
4(5 + 2) - 2(5) = 4(5) - 2
4(7) - 10 = 20 - 2
28 - 10 = 18
18 = 18 The solution works!