Expressions
Write -1/3(9x - 15) in expanded form.
-3x + 5
Solve the equation.
30 = 2(x + 3)
x = 12
When do you have to reverse the inequality symbol when solving inequalities?
when the coefficient is negative
Write the expression using the fewest number of terms.
10x - 2x
8x
Which expression is equivalent to 3x + 2?
a. x + x + x + 1 + 1
b. x + x + 1 + 1 + 1
c. 3x + 6
d. 3 + x + 2
Which are equivalent to 3(2m - 4)?
a. 6m - 4
b. 6m - 12
c. 2m - 4 + 2m - 4 + 2m - 4
d. 5m - 7
e. 2(3m - 6)
b, c, e
Solve the equation.
-4x - 17 = -5
x = -3
Solve the inequality.
19 < 2x + 10
4.5 < x
or
x > 4.5
Olivier has $48.25 to spend on painting classes. Each class costs $6 plus a one-time registration fee of $6.25. Let the variable represent the number of classes. Write an equation that represents the number of classes Olivier can attend for $48.25?
6n + 6.25 = 48.25
Write an equation to represent the situation.
A theater charges $10 for admission, plus $2.50 per treat. How many treats can a person buy if they spent a total of $50?
10 + 2.50m = 50
Simplify.
2k + (-7k) + 3 + 4k + 2
-k + 5
or
-1k + 5
A square has a perimeter of 32 centimeters. What is the length of each side?
8 centimeters
Solve and graph the inequality.
-3 > -2x + 9
6 < x
or
x > 6
graph should have an open circle at 6 shaded to the right
Saanvi and Tyler each started solving the equation 5(x - 1) = 45.
One of them made an error. Who was it?
Saanvi 5(x - 1) = 45 Tyler 5(x - 1) = 45
x - 1 = 9 5x - 1 = 45
Tyler made the error. He didn't distribute the 5 to -1.
Sal purchased b bowls for $7.50 each and paid $15 for shipping. The total cost of Sal’s purchase was $75. How many bowls did he buy?
8 bowls
Write 24a - 18 in factored form. Use the greatest common factor.
6(4a - 3)
Sid bought a keychain for $6.75 and 3 shirts for x dollars each. The items cost a total of $31.50. Write and solve the equation.
6.75 + 3x = 31.50
x = 8.25
A fitness instructor has a goal to hike more than 75 miles. They have already hiked 20 miles. They plan to hike n miles each week for the next 6 weeks. Which inequality describes the number of miles the fitness instructor should hike each week to meet their goal?
6m + 20 > 75
Simplify the expression:
-4(3x + 2y) + 6(-2x - 5y)
-24x - 38y
Which of the following is a simplified version of 3 + 5(x + 2) = 12?
a. 8x + 16 = 12 b. 8x + 2 = 12
c. 5x + 5 = 12 d. 5x + 13 = 12
Describe the error and write the correct simplified expression.
20p - 4(3p + 8) + 22
20p - 12p + 32 + 22
8p + 54
When using the distributive property, 8 was multiplied by 4 instead of -4.
Correct simplified expression:
20p - 12p - 32 + 22
8p - 10
Find the mistake and then correct it.
-4(5r + 2) = 90
-20r - 8 = 98
-20r = 90
r = -4.5
The mistake is that 8 should have been added to 98 instead of being subtracted from 98.
Correct equation:
-4(5r + 2) = 90
-20r - 8 = 98
-20r = 106
r = -5.3
It is currently 78°F outside and the temperature is rising 2 degrees every hour. Alisha will only stay outside if it is 90°F or cooler. Solve the inequality 78 + 2h ≤ 90.
h ≤ 6
Which of the following is equivalent to 7x - 56 - 28x?
a. 7(3x + 8)
b. -7(3x - 8)
c. 7(3x - 8)
d. -7(3x + 8)
d
Lee scored 25 points in yesterday's game. That was 3 more than twice the number of points Alex scored.
Which equation can be used to find, a, the number of points Alex scored?
a. 25 + 3 = 2a c. 2(25) + 3 = a
b. 25 = 3 + 2a d. 2(25) = 3 + a
b