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2-1A Writing Equations
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
In Chapter 1 you translated phrases. Phrases are
translated into mathematical expressions. Sentences are
translated into equations or inequalities.
Phrase
The sum of 6 and a number
6 + n
Sentence The sum of 6 and a number
is fifteen.
6 + n = 15
Sentence Seven times a number
is less than 50.
7n < 50
When choosing a variable for an unknown, it may be helpful
to select a Sentences
letter that must
relates to the unknown value (for
example: let have
a represent
a verb!age).
When you translate from English to math, you must first
determine whether the given problem is an expression
(phrase) or a sentence. How
do you know
the difference?
A sentence
will have
a verb.
Some verbal expressions that suggest the equal sign are:
is
is as much as
is the same as
is identical to
3
times a number is 36.
= 36
3n
Identify the verb. Write the equal sign. Translate
the expression to the left of the verb. Translate the
expression to the right of the verb. The equal sign is
like a brick wall – nothing crosses to the other side.
Translate each sentence into an equation.
21 decreased by a number is 7.
21  n = 7
Twelve is the sum of nine and a number.
12 = 9  n
15 less than a number is 56.
n  15 = 56
Five times the number a squared is three times
the sum of b and c.
5a2 = 3 (b + c)
The verb is where you write the equal sign.
The equal sign is like a brick wall –
nothing crosses to the other side.
Example 1 Translate each sentence into an equation.
a. Four times n is the difference of 30 and n.
4n = 30 - n
b. Nine increased by a number is five squared.
9 + n = 52
c. Ten less than a number is fifty.
n – 10 = 50
d. The sum of two and a number is 9.
2+n=9
e. A number decreased by five is four squared plus six.
n - 5 = 42 + 6
f. The sum of a number and six, divided by three is eight.
n6
8
3
Example 2 Translate each sentence into an equation.
a. Fifteen more than z times 6 is y times 2 minus eleven.
6z + 15 = 2y - 11
b. Seven increased by a number is 21.
7 + n = 21
b
c. A number b divided by three is six less than c.  c  6
3
d. Twenty-seven times k is h squared decreased by 9.
27k = h2 - 9
e. Nine times a number subtracted from 95 equals 37.
95 – 9n = 37
f. Two plus the quotient of a number and 8 is 16.
n
2   16
8
A formula is an algebraic equation that relates two or
more quantities.
Example 3 Translate each sentence into a formula.
a. The perimeter of a rectangle equals two times the
length
=
length plus two times the width.
width
P = 2l + 2w P = 2l + 2w
length
b. In a right triangle, the sum of the squares of the
measures of the legs, a and b, is equal to the square of
(hypotenuse)
the hypotenuse c.
(leg)
c
a2 +
b2
=
c2
a
(leg)
b
c. The perimeter of a triangle is side a plus side b plus
side c.
P = a+ b + c
width
2-A2 Pages 74-76 #13-18,23-26,35-36,50-51,57-68.