What the Interval
Write the inequality x>4 in interval notation.
(4, ∞)
Solve: x + 9 = 21
x = 12
A rectangle has a width of 6 inches and a length of 11 inches. What is its perimeter
34 inches
A number plus 7 equals 15. Write and solve the equation.
x + 7 = 15
x = 8
A mathematical statement that contains an equals sign.
Equation
Write the inequality x ≤ -3 in interval notation.
(-∞, -3]
Solve: -x + 4 = 2x - 11
x = 5
The perimeter of a rectangle is 50 feet. The length is 5 feet more than the width. What are the dimensions?
Width = 10 feet
Length = 15 feet
Five times a number equals 35. Write and solve the equation.
5x = 35
x = 7
A mathematical statement that compares two quantities using symbols such as <, >, ≤, or ≥.
Inequality
Write the inequality -2 < x ≤ 6 in interval notation.
(-2, 6]
Solve: 4(2x - 3) = 3x + 15
x = 27/5
The perimeter of a rectangle is 74 meters. The length is 7 meters more than twice the width. What are the dimensions?
Width = 10 meters
Length = 27 meters
Three less than twice a number equals 17. Write and solve the equation.
2x - 3 = 17
x = 10
Terms that have the same variables raised to the same powers.
Like terms
Solve and write the answer in interval notation: 3x - 5 ≥ 10.
[5, ∞)
Solve: -3(x - 4) + 2x = 19
x = -7
The perimeter of a rectangle is 94 yards. The length is 5 yards less than three times the width. What are the dimensions?
Width = 13 yards
Length = 34 yards
Three times the sum of a number and 8 equals 30. Write and solve the equation.
3(x + 8) = 30
x = 2
Numbers that follow one another in order, such as 12, 13, and 14.
Consecutive integers
Solve and write the compound inequality in interval notation: -7 < 2x + 1 ≤ 9.
(-4, 4]
Solve: 2(3x - 5) - 4(x + 1) = 18
x = 16
The perimeter of a rectangle is 58 inches. The length is 4 inches more than one and one-half times the width. What are the dimensions?
Width = 10 inches
Length = 19 inches
Seven more than twice a number equals three times the number minus 5. Write and solve the equation.
2x + 7 = 3x - 5
x = 12
A mathematical phrase containing numbers, variables, and operations, but no equals sign.
Algebraic Expression