Interpret Parts
A group of 4 students goes to a museum. Each student pays $15 for admission, and the group pays $8 total for parking.
The total cost is represented by:
4(15) + 8
What does the 15 represent?
The cost of admission for one student.
Determine the number of solutions.
3x + 5 = 3x + 5
Infinitely many solutions.
Solve for x.
x + 9 = 17
x=8
What property is used?
3(x + 5) → 3x + 15
Distributive Property
A gym charges a $20 registration fee plus $8 per visit.
Write an equation for a total cost of $60, where v represents the number of visits.
8v+20=60
The expression 6x + 12 represents the total cost of going to a skating rink, where x is the number of people skating.
What does the 12 represent if it is a one-time fee?
The fixed or one-time fee.
Determine the number of solutions.
5x + 2 = 5x + 9
No solution.
Solve for x.
4x - 7 = 21
x=7
What property or process is used to change
4x + 3x - 5
into
7x - 5?
Combining like terms.
A plant was 12 cm tall when it was purchased. After 6 weeks, it was 42 cm tall.
The equation
6x + 12 = 42
represents the situation.
How many centimeters did the plant grow each week?
5 cm per week.
A family buys 5 movie tickets for $11 each and spends $18 total on snacks.
The expression is:
5(11) + 18
What does 5(11) represent?
The total cost of the movie tickets.
Determine the number of solutions.
4x - 7 = 2x + 9
One solution.
Solve for x.
3(x + 4) = 24
x=4
Consider the equation:
2(x + 3) + 4x = 18
Which is the correct first step?
A. 2x+3+4x=18
B. 2x+6+4x=18
C. 6x+3=18
D. 2x+7x=18
B
Solve for x.
ax + 7 = 35
x=28/a
The expression
7g + 5
represents the total cost of playing g games at an arcade, including a $5 entrance fee.
What does the 7 represent?
The cost of one game.
Which equation has infinitely many solutions?
A. 6x+4=6x−4
B. 3(x+2)=3x+6
C. 5x−1=2x+8
D. 7x+2=7x+5
B
Solve for x.
5x - 8 = 2x + 13
x=7
A student solves:
5x - 8 = 17
Step 1: 5x=25
Step 2: x=5
What operation justifies Step 1?
Add 8 to both sides / Addition Property of Equality.
The formula for distance is
d=rt
Solve the formula for t.
t=d/r
A school club rents a bus for $250 and pays $12 for each student attending a trip.
The total cost can be represented by:
12s + 250
Identify the variable, coefficient, and constant.
Variable: s
Coefficient: 12
Constant: 250
Which TWO equations have no solution?
A. 4x+7=4x+7
B. 5x−3=5x+8
C. 2(x+4)=2x+8
D. 6x+1=6x−5
E. 3x+4=10
B and D
Solve for x.
4 - 2(3x + 5) = 2x - 14
x=1
Solve the equation mentally enough to identify the step that does NOT belong.
6 - 2x = 4(x - 3)
A. 6−2x=4x−12
B. 18−2x=4x
C. 18=6x
D. x=6
The correct solution is x=3.
The formula
A=P+Prt
represents an investment formula.
Solve for t.
t=A−P/Pr