Translate each of the following statements into an equation, using x as the variable:
(a) 13 subtracted from twice a number gives 3.
(b) One fifth of a number is 5 less than that number.
(c) Two-third of number is 12.
(d) 9 added to twice a number gives 13.
(e) 1 subtracted from one-third of a number gives 1.
(a) 2x − 13 = 3
(b) x/5 = x − 5
(c) 2x/3 = 12
(d) 2x + 9 = 13
(e) x/3 − 1 = 1
Step 0: Let the unknown number be \(x\).
(a) “13 subtracted from twice a number gives 3.”
“Twice a number” means: \(2x\)
“13 subtracted from twice a number” means: \(2x - 13\)
“gives 3” means it equals 3: \(= 3\)
Equation: \(2x - 13 = 3\)
(b) “One fifth of a number is 5 less than that number.”
“One fifth of a number” means: \(\dfrac{x}{5}\)
“5 less than that number” means: \(x - 5\)
“is” means equals: \(=\)
Equation: \(\dfrac{x}{5} = x - 5\)
(c) “Two-third of a number is 12.”
“Two-third of a number” means: \(\dfrac{2x}{3}\)
“is 12” means it equals 12: \(= 12\)
Equation: \(\dfrac{2x}{3} = 12\)
(d) “9 added to twice a number gives 13.”
“Twice a number” means: \(2x\)
“9 added to twice a number” means: \(2x + 9\)
“gives 13” means it equals 13: \(= 13\)
Equation: \(2x + 9 = 13\)
(e) “1 subtracted from one-third of a number gives 1.”
“One-third of a number” means: \(\dfrac{x}{3}\)
“1 subtracted from one-third of a number” means: \(\dfrac{x}{3} - 1\)
“gives 1” means it equals 1: \(= 1\)
Equation: \(\dfrac{x}{3} - 1 = 1\)