Transcript Solving Equations Using Addition and Subtraction

Solving Equations Using
Addition and Subtraction
3.1
GOAL
1
ADDITION AND SUBTRACTION EQUATIONS
VOCABULARY
•equivalent equations
•inverse operations
•solution step
•linear equation
TRANSFORMATIONS THAT PRODUCE
EQUIVALENT EQUATIONS
•Add the same number to each side.
•Subtract the same number from each side.
•Simplify one or both sides.
•Interchange the sides.
EXAMPLE 1
Extra Example 1
x  9  17
Click to
see the
solution
EXAMPLE 2
Extra Example 2
Solve –11 = n – (–2)
Click to see the solution
Solution steps are written one below the other with the
equal signs aligned.
Linear equations: The variable is raised to the first power
and does not appear in a denominator, inside a square
root sign, or inside absolute value symbols.
Checkpoint
Solve 5 + x = –3. Check your solution.
x  8
3.1
GOAL
Solving Equations Using
Addition and Subtraction
2
USING LINEAR EQUATIONS IN REAL-LIFE
PROBLEMS
We will use techniques we’ve already learned to write
verbal models with labels, equations, and then to solve
the equations.
EXAMPLE 3
Extra Example 3
The normal high temperature in January in Bismarck, North
Dakota, is 20°F and the normal low temperature is –2°F.
How many degrees apart are the normal high and low
temperatures?
VERBAL
MODEL
LABELS
Click to see the solution
ALGEBRAIC
MODEL
SOLVE
CHECK
EXAMPLE 4
Extra Example 4
Match the real life problem with the equation.
x+7=9
x–2=7
9–x=7
a. You have x dollars and your friend repays you the $7 he
owes you. You now have $9. How much did you have
originally?
b. The temperature was x °F. It fell 2°F and is now 7°F.
What was the original temperature?
c. A 9 foot post extends x feet below ground and 7 feet
above ground. What is the length x buried below ground?
Click to see the solution
Checkpoint
“Your bank balance is $42. If you write a check to buy a
pair of shoes, your balance would be –$5. How much do
the shoes cost?”
Does the equation x + 42 = –5 model the situation? If not,
write an equation that does. Then solve the problem to find
the cost of the shoes.
No; 42 – x = –5; $47
QUESTIONS?