Solving Problems
Is 4x+7 an expression or an equation?
expression
3(x+2)=3x+6
Always
Solve: x+9=15
x=6
Solve A=lw for l.
Answer: l=A/w
Movie tickets cost $8 each. Write an expression for the cost of t tickets.
Answer: 8t
Is x=3 a solution to 2x+5=11?
yes
x+4=x−4
never
Solve: 4x−7=21
x=7
Solve d=rt for t.
Answer: t=d/r
You have $50 and spend $6 on each meal. Write an expression for the money remaining after buying m meals.
Answer: 50−6m
How many solutions does 5x+10=5(x+2) have?
infinite
x2=5x
sometimes, x= 0, 5
Solve: 3(x+2)=18
x=4
Solve 2x+3y=12 for y.
y=(12-2x)/3
A shirt costs $60 and is discounted by 25%. What is the sale price?
Answer: $45
How many solutions does 3x+7=3x−2 have?
no solutions
(x+4)2=(x−4)2
sometimes, x=0
Solve: 5−2x≥17
x≤−6
Solve for C.
F=9/5C+32
Answer:
C=5/9(F-32)
Three consecutive integers have a sum of 72. Find the integers.
Answer: 23, 24, and 25
Is 4(x+2)=2(2x+4) an identity? Explain.
yes, it has infinite solutions
x2−16=(x−4)(x+4)
Always
Solve: 3(x−2)+4<2(x+5)
x<12
Are 3(x−4)=18 and 3x−4=18 equivalent? Explain.
Answer: No. The first has x=10, while the second has x=22/3.
A bus can carry at most 3,600 pounds. Each passenger and their luggage weigh about 180 pounds total. The driver and supplies weigh 360 pounds. Write an inequality and find the maximum number of passengers.
Answer: 180p+360≤3600; maximum of 18 passengers.