Equations
The value x = 8 is NOT a solution to which of the following equations:
1. x - 5 = 3 3. 2x + 3 = 22
2. x + 6 = 2x - 2 4. 0.5x + 6 = x + 2
3. 2x + 3 = 22
3(x+4) - 15 = 21
3x + 12 - 15 = 21
Distributive Property
Solve the inequality for x.
3x + 9 < 30
x < 7
Write an equation for the following sentence.
The sum of a number and 5 is multiplied by -3 and the result is -42.
-3(x + 5) = -42
Solve for x.
2x - 10 < 30
x < 20
Which value below is a solution to the equation?
3(2x - 1) = 4(x + 1)
1. 1/4 3. 3.5
2. 2.75 4. 2/7
3. 3.5
Which property is being used?
3x + 12 - 15 = 21
3x + (12 - 15) = 21
Associative Property
Solve the inequality for x.
850 - 38m ≥ 223
m ≤ 16.5
At the beginning of the month an oil tank contained 350 gallons of oil. A furnace uses oil at a rate of 8.5 gallons per day. Which equation below could be solved to determine how many days, d, it will take for the furnace to have 75 gallons left in it?
(1) 8.5d + 350
(2) 350 - 8.5d = 75
(3) 8.5 - 350d = 75
(2) 350 - 8.5d = 75
The circumference, C, of a circle is given by the formula C = 2πr, where r is the circle's radius. Which of the following is the result when solved for r?
(1) r = C - 2π
(2) r = (C/2) - π
(3) r = C/(2π)
(3) r = C/(2π)
Solve for x algebraically. Check your solution.
3x - 4 = 23
x = 9
Check:
3(9)-4 = 23
23 = 23
Sofia manipulated the equation 4x + 7 = 10 by adding -7 to both sides. Which of the following properties justifies this manipulation?
1. associative property of addition
2. addition property of equality
3. commutative property of addition
4 multiplication property of equality
2. addition property of equality
Solve the inequality for x.
-4(x - 7) + 25 < 5
x > 12
or
12 < x
Lauren has $120 saved up to buy books. If each book, b, costs $15, which inequality represents the possible number of books that Lauren can buy?
(1) b > 8
(2) b > 105
(3) b < 10
(4) b ≤ 8
(4) b ≤ 8
Which is a solution to (n-3)/5 = -2
(1) n = -11
(2) n = -7
(3) n = 3
(2) n = -7
Is x = 8 a solution to the following equation? State yes or no. Justify.
-2x + 4 = 3(4-x)
-2(8)+4 = 3(4-8)
-12 = -12
Yes, x = 8 is a solution.
Which property is being used?
5x - 8 = 12
5x - 8 + 8 = 12 + 8
Addition Property of Equality
What is the smallest integer solution to the inequality?
6x + 2 > 2x + 23
6
because x > 5.25 and 6 is the next integer greater than 5.25
Water is being drained from a swimming pool at a rate of 780 gallons per hour. The swimming pool initially contained 45,000 gallons of water. A chemical must be added when it has about 15,000 gallons of water remaining. Write an equation to represent the situation. Use a let statement for your variable.
let x = number of hours
45000 - 780x = 15000
Two consecutive, odd integers have the property that six more than twice the larger is four times the smaller. If n represents the smaller of the two integers, which of the equations models the information?
1. 2(n + 1) + 6 = 4n
2. 2n + 6 = 4(n+2)
3. 2(n+2) + 6 = 4n
3. 2(n + 2) + 6 = 4n
Find the solution algebraically. Check your solution.
2(4x + 7) = -4(3x - 1)
x = -0.5
Check:
2(4(-0.5)+7) = -4(3(-0.5)-1)
10 = 10
Which property is being used?
5x = 20
5x / 5 = 20 / 5
Division Property of Equality
Solve for x.
2(x + 2) < -2x - 1
x < -1.25
A hot air balloon at a height of 850 feet starts to move towards the ground at a rate of 38 feet per minute. People in the hot air balloon can see a distant lake when they are at least 223 feet above the ground. Write an inequality that models when the people can see the lake. Use m to represent the number of minutes.
850 - 38m ≥ 223
If the expression shown is solved for x in terms of a, b, and c, then solve for x.
2x/a + b = c
x = (ac - ab) / 2