Download 6.2 Linear Equations in One Variable

Linear Equations in One Variable
- We will solve linear equations
- We will solve linear equations containing
fractions.
- We will solve a formula for a variable.
- We will identify equations with no solution or
infinitely many solutions
Equivalent Equations
• Equivalent equations – When you take an
original equation and perform the same
transformation to both sides.
- We will solve linear euqations.
Solving Linear Equations in One Variable.
The Multiplication Property of Equality
Showing Multiplication on a balance
• 2x = 14
Using Properties of Equality to Solve Equations.
Solving a Linear Equation
- We will solve linear equations with fractions
Solving Linear Equations Involving Fractions.
Using a Formula for a Given Result
- We will solve a formula for a variable.
Solving a Formula for a Variable
Solving a Formula for a Variable
- We will identify equations with no solutions or infinitely many solutions.
Parallel Equations
Applications of Linear Equations
• We will use linear equations to solve
problems.
• We will ascertain linear equations from word
problems.
- We will use linear equations to solve problems.
Problem Solving with Linear Equations
Strategy for solving word problems
1. Read the problem carefully at least twice. Attempt to state
the problem in your own words and state what the problem is
looking for. Let x (or any variable) represent one of the
quantities in the problem.
2. If necessary, write expressions for any other unknown
quantities in the problem in terms of x.
3. Write an equation in x that models the verbal conditions of
the problem.
4. Solve the equation and answer the problem’s question.
5. Check the solution in the original wording of the problem, not
in the equation obtained from the words.
Converting Words to expressions
• 4 times what number gives 20?
• What number divided by 5 gives 2?
• What number minus 8 gives 4
• What number cubed gives 27
• What number plus 4 gives 16
• Pg 324 in your book has a more complete list.
- We will ascertain linear equations from word problems.
Modeling for a word problem
• How much will it cost for you to drive to San Francisco,
California from North Smithfield, Rhode Island? The trip is
3700 miles and your car will average 30 miles/gallon on the
highway. The national average for gasoline is 3.84.
• How many times will you have to stop for gas is your tank is 17
gallons?
Assigning x to a variable in a word problem.
• The sum of three consecutive odd numbers is
21, what are the three numbers?
Assigning the correct meaning to x
• A coach will order baseball caps from one of two companies.
– Creative Caps charges a one time fee of $50, plus $5 per
baseball cap.
– Happy Hats charges a one-time fee of $30, plus $6 per
baseball cap.
a. Write an algebraic expression to represent the amount that each company charges
for an order of baseball caps.
b. The coach wants to buy baseball caps from the least expensive company. In terms of
the number of baseball caps, when should the coach order the baseball caps from
Creative Caps?