Objective- To recognize symbols, variables, and types of sentences used in algebra.

Equalities Inequalities

= Equals- is the same as

Congruent- same size and shape

Similar- same shape

< Is less than

> Is greater than

Is less than or equal to

Approx. equal to

= Not equal to

~

Expressions vs. Equations

Numerical

Variable

Expressions Equations Inequalities

2 + 35(8) - 4

x + 78 - 3y

2 + 3 = 54 + 2(3) = 10

x - 4 = 1311= 3 + 2m

9 - 5 > 3

6y - 4 < 8

Sentences

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

2) 7 < 2(5) + 3

3) 5x - 2

4) 6m + 2 > 3

Sentence, open sentence, equation

Sentence, inequality

Expression

Sentence, open sentence, inequality

Open sentences have solutions and can be solved.

Variable Equations Variable Inequalities

4 + m = 7 5 + y < 91- 4 - 4

m = 3

- 5 - 5

y < 86

One Solution InfiniteSolutions

Give three solutions to each sentence below.

1) x > 10

2) x + 3 7

3) 5 - x < 0

4) 2 1 3x

Samples: 11, 15, 34

Samples: 4, -8, 0

Samples: 6, 7, 10

Samples: 3, 4, 7

Objective - To translate English words, phrases, and sentences into mathematical symbols, expressions, and equations respectively.

+ _ plusadd

increased bysum

more than

minussubtract

decreased bydiminished by

less thansubtracted from

differenceless

total

product…of...

twice ( 2)

timesmultiply

dividequotient

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 is less than x 5 < x

5 less than x x - 5

5 subtracted from x x - 5

Translate each phrase into a mathematical expression.

1) 5 subtract x

2) the product of 10 and y

3) 20 decreased by a number 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

5 - x

10y

20 - t

11m + 6

y 9

7k - 8

Translate each phrase into a mathematical expression.

1) six less than twice a number x

2) five times the sum of y and 4

3) twice the difference of m and 3

4) the quotient of 7 and a number x less 2

5) the difference of 6 and k divided by 9

6) 4 times the sum of 12 and y

2x - 6

5(y + 4)

2(m - 3)

(6 - k) 9

7 x - 2

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) Six more than x is more than twice the difference of x and 7.

3) The quotient of m and 3 is six less than theproduct of 10 and m.

4) Five less than x is less than five less x.

2(4 + y) - 8 = 19

x + 6 > 2(x - 7)

x - 5 < 5 - x

m 3 = 10m - 6