Algebraic Translations
the sum of 5 and a number x
5 + x
In algebraic translations, what operation does the word “sum” indicate?
Addition (+)
Evaluate x + 7 when x = 5.
12
Solve: x + 7 = 15
x = 8
Solve for x: x + 5 = y
x = y − 5
7 less than a number n
n − 7
What operation does the word “product” indicate?
Multiplication (×)
Evaluate 3x − 4 when x = 6.
14
Solve: x − 12 = 5
x = 17
Solve for y: x + y = 12
y = 12 − x
three times the sum of a number x and 4
3(x + 4)
In the phrase “5 less than a number x,” which operation is used, and what is the expression?
Subtraction; x − 5
Evaluate 2x² + 3 when x = 4.
35
Solve: 4x = 28
x = 7
Solve for x: y = 3x + 4
x = (y − 4)/3
the difference of twice a number y and 9
2y − 9
What does the word “of” usually mean in an algebraic expression?
Multiplication
Evaluate 3x² − 2y when x = 3 and y = 5.
17
Solve: 3x + 5 = 20
x = 5
Solve for r: A = πr²
r = √(A/π)
five less than twice the sum of a number x and 3
2(x + 3) − 5
What does the word “is” usually represent in an algebraic translation? Give an example.
Equals (=); “A number x plus 4 is 10” → x + 4 = 10
Evaluate 2(x + 4)² − 3x when x = 2.
69
Solve: 7x − 9 = 33
x = 6
Solve for h: A = ½bh
h = 2A/b