Objective- To recognize symbols, variables,
and types of sentences used in algebra.
Equalities
= Equals- is the
same as
 Congruent- same
size and shape
~ Similar- same
shape
Inequalities
< Is less than
> Is greater than
 Is less than or
equal to
 Approx. equal to
= Not equal to
Expressions vs. Equations
Sentences
Expressions
Numerical
Variable
2+3
5(8) - 4
x+7
8 - 3y
Equations
2+3=5
4 + 2(3) = 10
x - 4 = 13
11= 3 + 2m
Inequalities
9-5>3
6y - 4 < 8
Open sentences
Open sentences have solutions and can be solved.
Identify each as an expression, sentence,
open sentence, equation, or inequality.
1) 3x + 5 = 11
Sentence, open sentence, equation
2) 7 < 2(5) + 3
Sentence, inequality
3) 5x - 2
Expression
4) 6m + 2 > 3
Sentence, open sentence, inequality
Open sentences have solutions and can be solved.
Variable Equations
4+m=7
-4
-4
m=3
One Solution
Variable Inequalities
5 + y < 91
-5
-5
y < 86
Infinite
Solutions
Give three solutions to each sentence below.
1) x > 10
Samples: 11, 15, 34
2) x + 3  7
Samples:
4, -8, 0
3) 5 - x < 0
Samples:
6, 7, 10
4) 2x  1  3
Samples:
3, 4, 7
Objective - To translate English words, phrases,
and sentences into mathematical symbols,
expressions, and equations respectively.
_


+
minus
times
divide
plus
subtract
multiply
quotient
add
increased by decreased by product
diminished by …of...
sum
difference
twice ( 2)
total
less
more than
less than
subtracted from
Tricky Ones!
5 plus x
5+x
add 5 and x
5+x
the sum of 5 and x
5+x
5 increased by x
5+x
5 more than x
x+5
5 is more than x
5>x
Tricky Ones!
5 minus x
5-x
5 less x
5-x
the difference of 5 and x
5-x
5 decreased by x
5-x
5 less than x
x-5
5 subtracted from x
x-5
5 is less than x
5<x
Translate each phrase into a mathematical expression.
1) 5 subtract x
5-x
2) the product of 10 and y
10y
3) 20 decreased by a number t
20 - t
4) 6 added to the product of 11 and m
5) the quotient of y and 9
6) 8 less than 7 times k
y
7k - 8
9
11m + 6
Translate each phrase into a mathematical expression.
1) six less than twice a number x
2x - 6
2) five times the sum of y and 4
5(y + 4)
3) twice the difference of m and 3
2(m - 3)
4) the quotient of 7 and a number x less 2
7 x-2
5) the difference of 6 and k divided by 9
(6 - k) 9
6) 4 times the sum of 12 and y
4(12 + y)
Translate each sentence into a mathematical
equation or inequality.
1) Eight less than twice the sum of four and y
is the same as 19.
2(4 + y) - 8 = 19
2) Six more than x is more than twice the
difference of x and 7.
x + 6 > 2(x - 7)
3) The quotient of m and 3 is six less than the
product of 10 and m.
m 3 = 10m - 6
4) Five less than x is less than five less x.
x-5<5-x