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Solving for x
December 7, 2010
Solving for x
• When solving an equation, the goal is to get the
variable by itself on one side of the equation.
• Inverse operations are the same as opposite
operations.
• Addition and subtraction are inverse operations.
• Multiplication and division are inverse operations.
Solving for x
• variable term – the term containing a variable.
• number term – the term containing only a number.
• If the number term is positive, subtract it from both
sides of the equation.
• If the number term is negative, add its positive
value to both sides of the equation.
One-Step Equations
• A one-step equation is as straightforward as it
sounds. You will only need to perform one step in
order to solve the equation.
One-Step Equations
• One goal in solving an equation is to have only
variables on one side of the equal sign and numbers
on the other side of the equal sign. The other goal
is to have the number in front of the variable equal
to one.
One-Step Equations
• Solve x + 5 = -17
• Subtract 5 from both sides, or flip 5 to the other side.
Subtract
Flip
x + 5 = -17
x + 5 = -17
-5 -5
x = -17 - 5
x = -22
x = -22
Two-Step Equations
• A two-step equation is as straightforward as it
sounds. You will need to perform two steps in order
to solve the equation.
• In solving two-step equations you will make use of
the same techniques used in solving one-step
equation only you will perform two operations
rather than just one.
Two-Step Equations
• Solve 3x + 4 = 13
Subtract
3x + 4 = 13
- 4 -4
3x = 9
3 3
x=3
Flip
3x + 4 = 13
3x = 13 - 4
3x = 9
3 3
x=3
Two-Step Review
• Move the number term by either adding it or
subtracting it on both sides of the equation.
• Move the coefficient by dividing by the coefficient
on both sides of the equation.
Multi-Step Equations
• In multi-step equations, you will need to make use of
the techniques used in solving one-step and two-step
equations.
• Just as with solving one-step or two-step or any
equation, one goal in solving an equation is to have only
variables on one side of the equal sign and numbers on
the other side of the equal sign. The other goal is to
have the number in front of the variable equal to one.
Keep in mind that the variable does not always have to
be x. These equations can make use of any letter as a
variable.
Multi-Step Equations
• Solve 4x + 9 = 2x – 5
Subtract
4x + 9 = 2x – 5
-2x
-2x
2x + 9 = -5
-9 -9
2x = -14
2
2
x = -7
Flip
4x + 9 = 2x - 5
4x – 2x + 9 = -5
2x + 9 = -5
2x = -5 – 9
2x = -14
2
2
x = -7
Multi-Step Review
• Combine like terms on each side.
• Get the variable terms on the same side of the equation.
– Add or subtract the one variable term to get it to the side of the
variable term with the larger coefficient.
• Move the number term by adding or subtracting.
– Add if the number term is negative.
– Subtract if the number term is positive
• Move the coefficient by dividing.
• If the variable terms cancel on both sides the answer is no
solution.
• If all terms and coefficients cancel on both sides (nothing is
left), the answer is any number.