Solving Equations

2-Step Equation

After studying this lesson, you will be able to:

• Solve equations that require two steps.

Review of Steps for Solving Equations:

1. Remove parentheses by multiplying (this step is not always necessary)

2. Collect like terms on each side of the equal sign

3. Isolate the variable by "undoing" the operation (do this until the variable is by itself)

1. "undo" addition and subtraction first
2. next, "undo" multiplication and division

4. Check by substituting the solution into the original equation

Example 1

3x + 4 = 10	This equation will require 2 steps to solve it
3x + 4 -4 = 10 -4	First, we need to "undo" +4 so we subtract 4 from each side. This gives us 3x = 6
	Now, we need to "undo" 3 times x, so we divide each side by 3
x = 2	Now, we have the solution

Check:

substitute 2 for x in the original equation

3 (2) + 4 = 10

6 + 4 = 10

10 = 10 (notice that it also required 2 steps to check)

Example 2

-2x - 6 = 12	This equation will require 2 steps to solve it
-2x - 6 + 6 = 12 + 6	First, we need to "undo" -6 so we add 6 to each side This gives us -2x = 18
	Now, we need to "undo" -2 times x, so we divide each side by -2
x = -9	Now, we have the solution

Check: substitute -9 for x in the original equation

-2 (-9) -6 = 12

18 - 6 = 12

12 = 12

Example 3

	This equation will require 2 steps to solve it
	First, we need to "undo" +9 so we subtract 6 from each side This gives us
	Now, we need to "undo" (which is x divided by 4), so we multiply each each side by 4.
x = -12	Now, we have the solution

Check:

substitute -12 for x in the original equation

-3 + 9 = 6

6 = 6

Example 4

	In this equation, keep in mind that the expression 2-3x is being divided by 4 Since we're dividing an entire expression by another number, we need to deal with that first.
	First, we need to "undo" the divided by 4 so we multiply each side by 4 This will eliminate the division and therefore simplify our equation. Notice that on the right-hand side, the fours cancel out each other
48 = 2-3x	After multiplying both sides by 4 we get to this equation
48 -2 = 2-3x -2	Now, we need to "undo" the 2 (positive 2) so we subtract 2 from each side (Remember, we are trying to isolate the variable - get the x by itself, so we Need to get rid of the 2 first.) This will give us 46 = -3x
	To "undo" the -3 times x, we divide each side by -3
	This is the solution