- To solve an equation with one variable like 3x + 2 = 11, the first step is to isolate the variable by using its additive inverse. For this equation, subtract 2 from both sides. The second step is to divide both sides by the coefficient of x, which is the multiplicative inverse. - A solution to an equation makes the equation true. For example, in x + 2 = 3, x = 1 is the solution that makes the statement true. - Additive inverses are used to isolate the variable by adding or subtracting them. Multiplicative inverses are used to isolate the variable by dividing or multiplying. We assume they equal 0 and 1, respectively, to simplify isolating the

1. SOLVING EQUATIONS WITH
ONE VARIABLE

2. HOW WOULD YOU START TO SOLVE AN
EQUATION? ( HYPOTHETICAL QUESTION)
• If you were given the equation 3x + 2 = 11, what would be your first step to
solving it?
• Your second step?
• Can you reverse the order of the steps?

3. EQUATIONS
• A Solution to an equation is a value or set of values that makes
the equation true.
• Ex) In the equation x + 2 = 3, x =1 since 1 + 2 = 3

4. ADDITIVE INVERSES
• The Additive inverse is what you need to add to a number to
make it equal to zero.
• 2 + (-2) =0

5. ADDITION/SUBTRACTION
• 7 + x = 20
• Isolate the variable by adding the additive inverse.
• 7 -7 + x = 20 -7
• x = 13

6. MULTIPLICATIVE INVERSES
• What you need to multiply a number by to equal 1.
• 2 x ½ =1
• -2/3 x -3/2 =1
• Why do you assume that the Additive inverse equals 0 and the
multiplicative inverse equals 1? (Assumption question)

7. MULTIPLICATION/DIVISION
• 4x = 16
• Isolate the variable by multiplying by the multiplicative
inverse,1/4, or dividing by 4
• 4(1/4)x = 16(1/4)
• x = 4

8. MULTIPLE OPERATIONS
• 3x + 6 + 4x = 13
• 7x + 6 = 13 (Combine like terms, 3x+4x = 7x)
• 7x = 7 (Isolate the variable by subtracting 6 from both sides,
because 6 and -6 are additive inverses)
• X=1 (Multiply both sides by the multiplicative inverse, 1/7, or
divide both sides by 7)

9. CHECKING YOUR WORK
• You can check your work by plugging your answer back into
the original equation and seeing if it is equal.
• Ex) 3x + 6 + 4x = 13
• 3(1) + 6 + 4(1) = 13
• 3 + 6 + 4 = 13
• 13 = 13

10. TRY THESE QUESTIONS(REASON AND
EVIDENCE QUESTION)
• 3 - 5x = 18
• -4 +2x = 10
• 6x + 3 = 9
• -8x + 10 =6