Solving Equations Lesson 1 – Making Zero

Activity #17: Solving Equations – Reading and Interpreting equations
Lesson: How can we describe mathematical equations verbally and/or orally? How
can we be so precise with language that we can perfectly describe an equation to
another person?
How do we describe (in words) the mathematical expression: x + 5?
What about the full equation: 2(x – 3) = –12?
Study the examples below:
Literal description
“A number increased by 5”
“5 is added to a number”
“A number is decreased by 5”
“5 less than a number”
“The product of a number and 5”
“A number increases by a factor of 5”
x ÷ 5 or x 5
“A number is split 5 ways”
“The quotient of a number and 5”
“The sum of a number and 5 is 12”
x + 5 = 12
2(x - 5) = 12
x2 = 144
x3 = 27
x + y = 10
“Twice the difference of a number and 5
is 12”
“A number squared is 144”
“A number cubed is 27”
“The square root of a number is 8”
“The sum of two numbers is 10”
Rewrite each of the following as an algebraic equation. Then, solve the equation.
a) A number squared less nineteen equals two hundred six.
b) Four and one-half times a number plus eight equals one and one-half times the
same number less six.
c) One-quarter times a number equals six-elevenths.
d) Four times the quantity of a number less five equals seven times the quantity of
the same number plus one.
e) Four times a number is twenty
f) A number increased by four gives twenty-one.
g) The square of a number is twenty-five.
h) A number decreased by ten equals two.
i) Five less than a number is nine.
j) The product of a number and six is twenty-four.
k) The quotient of a number and ten is five.
l) Three more than a number is eighteen.
m) A number increased by seven is tripled giving twenty-two.
n) Two less than five times a number is equal to negative eighteen