Module One Review
Evaluate 3² + 2(7 - 4).
Answer: 15
3^2 +2(7-4)
9 + 2(3)
9 + 6
15
Solve 4x - 9 = 19.
Answer: 7
4x-9=19
4x=28
x=7
How many solutions does 3x + 5 = 17 have? Find the solution if there is one.
Answer: One solution: x = 4
3x + 5 = 17
3x=12
x=4
Solve 3x + y = 18 for y.
y = 18 - 3x.
3x + y = 18
y=18-3x
Solve |x| = 9 .
Answer: x = 9 and = -9.
A bowling alley charges $6 for shoes plus $4 per game. Write an expression for the total cost of g games.
Answer: 6 + 4g dollars.
Which property changes 8 + (x + 5) to (8 + x) + 5?
Answer: Associative property of addition.
The grouping changes; the order does not.
Solve 0.25x + 6 = 18 - 0.5x.
Answer: x = 16.
0.25x + 6 = 18 - 0.5x.
0.75x + 6 = 18
0.75x = 12
x=16
How many solutions does 4(x - 3) = 4x + 1 have? Find the solution if there is one.
Answer: No solution.
4(x - 3) = 4x + 1
4x-12=4x+1
-12=1
No solution, equation is false.
Solve 5a - 2b = 14 for b.
Answer: b = (-14+5a)/2 .
5a - 2b = 14
-2b=14-5a
b = (-14+5a)/2
Which equation has solution set {-6, 4}?
A: |x - 1| = 5
B: |x + 1| = 5
C: |x + 5| = 1
Answer: B: |x + 1| = 5
x + 1 = 5 x + 1 = -5
x=4 x = -6
Plan A costs $24 plus $5 per month. Plan B costs $8 plus $7 per month. Their costs are equal when m = 8. Interpret the solution and find the equal cost.
Answer: After 8 months, both plans cost $64
24+5m=8+7m
24=8+2m
16=2m
m=8
24+5(8)=$64 8+7(8)=$64
A student changes 5x - 12 = 23 to 5x = 35.
Name the property.
Answer: Addition property of equality
Solve 5(2x - 3) + 7 = 7x + 13.
Answer: x = 7
5(2x - 3) + 7 = 7x + 13.
10x-15+7=7x+13
3x-8=13
3x=21
x=7
How many solutions does 6(x + 2) - 3x = 3x + 12 have? Justify.
Infinitely many. Both sides simplify to 3x + 12; 12 = 12 is always true.
Solve P = 2l + 2w for l.
Answer: l =1/2P-w .
P = 2l + 2w
P-2w=2l
(P-2w)/2 =l
1/2P-w=l
Solve 3|2x + 1| = 15.
Answer: x = 2 and -3.
3|2x + 1| = 15.
|2x + 1| = 5
2x + 1 = 5 2x + 1 = -5
2x=4 2x=-6
x=2 x = -3
Shop A charges $35 plus $8 per hour. Shop B charges $59 plus $5 per hour. Write and solve an equation to determine the number of hours for which the total cost at both shops is the same.
Explain what your solutions means in this situation.
Answer: 35+8h=59+5h ; cost are equal after 8 hours; $99
35+8h=59+5h
35+3h=59
3h=24
35+8(8)=$99 59+5(8)=$99
Simplify 6(2x - 5) - 4(x + 3).
Answer: 8x -42
6(2x - 5) - 4(x + 3)
12x-30 -4x-12
12x-4x-30-12
8x-42
Solve 2/3x - 5 = 1/6x + 2.
Answer: x = 14.
2/3x - 5 = 1/6x + 2.
1/2x-5=2
1/2x=7
x=14
Determine the number of solutions and solve: 2(3x - 4) = 5x + 9.
One solution, x = 17. 6x - 8 = 5x + 9.
Solve A = 2πr² + 2πrh for h.
Answer: h = (A - 2πr²)/(2πr)
A = 2πr² + 2πrh
A-2πr²=2πrh
(A-2πr²)/(2πr)=h
(A)/(2πr)-r=h
Solve -2|3x - 4| + 6 = -10.
Answer: x = 4 or -4/3.
-2|3x - 4| + 6 = -10.
-2|3x - 4| = -16
|3x - 4| = 8
3x-4=8 3x-4=-8
3x=12 3x=-4
x=4 x=-4/3
A school sells adult tickets for $8 each and student tickets for $5 each. A total of 120 tickets are sold for $750.
Let x represent the number of adult tickets sold. Write an equation that can be used to determine the number of adult tickets sold.
Answer: 8x+5(120-x)=750
8x : adult tickets
5(120-x) student ticket money
750 amount of money made
Evaluate 2a² - 3b + ab when a = -3 and b = 4.
Answer: -6
2(-3)^2-3(4)+(-3)(4)
2(9)-12-12
18-12-12
6-12
-6
Solve 9x = 4(2 - x) + 3x.
x = 4/5. 9x = 8 - x; 10x = 8.
9x = 4(2 - x) + 3x.
9x=8-4x+3x
9x=8-x
10x=8
x=8/10 = 4/5
Find the value of k that makes the equation have infinitely many solutions.
5(x-2)=5x+k
Answer: k= -10
Solve ax + bx = c for x.
Answer: x = c/(a + b)
ax + bx = c
x(a+b)=c
x=c/(a+b)
Solve 4|2x - 7| + 9 = 1
Answer: No solution because an absolute value cannot be negative.
4|2x - 7| + 9 = 1
4|2x - 7| =-8
|2x - 7| =-2
Three consecutive integers have a sum of 81.
Write and solve an equation to find the middle number.
Answer: 27
Let x = the middle number
(x-1)+x+(x+1) =81
3x = 81
x= 27
(x-1) = 27-1= 26
x= 27
(x+1)=27+1 =28
The three numbers are 26, 27, 28