Transcript 1-4 Equations and Inequalities

3-3 HW: Pg. 148-152 #10-50eoe,65, & Quiz 1 Pg. 152 #1-11
10.) no
22.) x=-12
14.) yes
26.) x=-3
38.) x=-1
18.) x=12
30.) x=1 1/2
34.) x=15
42.) The left side was simplified incorrectly. Answer should be -1 2/3
46.) x=64
50.) a. If n is an integer, the next two consecutive integers are n+1 and
n+2
b. 27, 28, and 29
65.) a. 2/7, 2/7t
b. 3/14 t
c. 2/7 t + 3/14 t
d. 1 represents the entire job, so letting t=time it takes to do the whole
job, the fraction of the work Luis can do in that time (2/7 t) plus the
fraction for Mei (3/14 t) equals the whole job.
Quiz 1 Pg. 152 #1-11
1.) y = 17
2.) x = 4 ½
3.) z = -2
4.) b = 5/8
5.) q = 32
6.) n = 3
7.) x = -46
8.) y = 12
9.) x = -5
10.) x + 4 = 91. I would have earned 87 points
without the bonus points.
11.) 22 2/9 degrees Celsius is the equivalent
temperature.
Wir2.5
• LESSON
3-4 Solving Equations with Variables
On Both Sides
Still use the OPPOSITE OPERATION!
• Collect the variable terms on the side with the greater
variable coefficient
• Linear equations do not always have one solution.
Some have no solution!
• A identity is an equation that is true for all values of
the variable.
Practice
Solve the equation by showing work on BOTH sides
if possible. Does the equation have one solution, is
it an identity, or does it have no solution?
1.) 2x+3=7x
3.) x-2x+3  3  x
2
5.) (6c+3)=6(c-3)
3
2.) 12-2a=-5a-9
4.) 5x+24  5( x  5)
6.) 6y-(3y-6)=5y-4
Answers :
3
1.) x= ; one solution
2.) a=-7; one solution
5
3.) all real numbers; an identity 4.) no solution
5.) c = 10; one solution
6.) y=5; one solution
Practice 2
1.) A video store charges $8 to rent a video game for five days. You
must be a member to rent from the store, but the membership fee is
free A video game club in town charges only $3 to rent a game for
five days, but membership in the club is $50 per year. Which plan is
more economical?
2.) You are making pies to sell at a fundraiser. It costs $3 to make each
pie, plus a one-time cost of $20 for a pastry blender and a rolling
pin. You plan to sell the pies for $5 each. Write an equation to find
the number of pies you need to sell to break even.
Answers:
1.) x  # rented
8x=3x+50
x=10
So if you rent 10 in a year, the cost would be the same, but if you rent more than
10 the club is more economical. Less than 10, the store is more economical.
2.) x = #pies needed to break even
3x+20=5x
x = 10 pies
So I would need to sell 10 pies to break even.
Summary
• Is the equation -2(4-x)=2x-8 an identity? Explain why or
why not.
• Ans: Yes, it is an identity because it is true for all values
of x since the left side equals the right side.
• Decide if the state is true or false. The solution of x=2x is
zero.
• Ans: True
• Solve 9(9-x)=4x-10. Explain each step along the way.
9  9  9 x  4 x  10
81  9 x  4 x  10
distribute
simplify
-4x -4x
81-13x=-10
-81
-81
-13 -91
x=
-13 -13
x=7
move the x's on same side
simplify
move the constants on same side
simplify & divide both sides by -13
Check Yourself
Pg. 157-159 #12-42e, 56-64 e
• #12-42: solve the equation and SHOW WORK
on BOTH SIDES
• #56-64: mixed review
Day 2: Pg. 157 #19-41 odd