Transcript Solving Equations with Variables on Both Sides

Solving Equations with
Variables on Both Sides
3.4
GOAL
1
COLLECTING VARIABLES ON ONE SIDE
The technique: Find the variable with the largest coefficient,
and collect its like terms on that side of the equation.
EXAMPLE 1
EXAMPLE 2
Extra Example 1
Solve:
6 x  22  3 x  31
Click to see the solution
Extra Example 2
Solve:
64  12w  6w
Click to see the solution
Some equations have infinitely
many solutions and are called
identities, and some equations
have no solutions.
EXAMPLE 3
Extra Example 3
a. Solve
4( x  5)  4 x  20
Click to see the solution
Extra Example 3
b. Solve
3x  9  3x  10
Click to see the solution
EXAMPLE 4
Extra Example 4
a. Solve the equation.
3
10(2  x )  4 x   ( x  3)
10
Click to see the solution
Extra Example 4 (cont.)
b. Solve the equation.
2
(10 x  15)  18  4( x  3)
5
Click to see the solution
Checkpoint
Solve each equation.
1.
17  2 x  14  4 x
1
x
2
2.
2(3 x  4)  6 x  9
no solution
Checkpoint (cont.)
3. Solve the equation.
1
(12  2 x )  4  5 x  2( x  7)
2
x2
3.4
GOAL
Solving Equations with
Variables on Both Sides
2
SOLVING REAL-LIFE PROBLEMS
EXAMPLE 5
Extra Example 5
A gym offers two packages for yearly membership. The
first plan costs $50 to be a member. Then each visit to the
gym is $5. The second plan costs $200 for a membership
fee plus $2 per visit. Which membership is more
economical? Hint: Find the number of visits for which the
two plans will cost the same.
Click to see the solution
Checkpoint
One CD music club charges a $30 membership fee plus
$10 per CD. Another club charges $15 per CD but has no
membership fee. Which club is more economical?
The cost is the same for 6 CDs. If more than 6 are
purchased, the club with the $30 membership fee is more
economical. If fewer than 6 are purchased, the club
without a membership fee is more economical.
QUESTIONS?