3x + 1 = 7

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Name:_______________________________

3.1 Introduction to Algebra: Vocabulary

Equation

: a math sentence that states two quantities are ___________ .

It will have an _____________________ .

3x + 1 = 7

The equation says: what is on the left ( ) is equal to what is on the right ( ).

Parts of an Equation

Variable: a ____________ that represents a number we do not know yet.

3x + 1 = 7

!!! Every variable has a _________________

Coefficient: the number ____________________ the variable.

Can be __________________ or __________________ .

Constant: a number with no ________________ attached.

Term – any of the following:

single number (constant) single variable the product of a number (coefficient) and variable(s).

What coefficient does this variable have?

2k + 15 – m – 3 + n – 7p

Terms: ______________________________

Variables: ____________________

Coefficients: _________________

Constants: ____________________

– 8 – 4c + 7 – c – 12c – 2

Terms: ______________________________

Variables: ____________________

Coefficients: _________________

Constants: ____________________

EXPRESSION: a group of terms. Contains numbers, __________________, and variables.

DOES NOT contain an _________________________ .

Label the parts of the expression: Coefficient, Constant, Variable

1.

8y – 7 + 2y

How many TERMS are present in this expression? ____ List them: ________________________

2.

m + 4 + 2 – 7m + 6

How many TERMS are present in this expression? ____ List them: ___________________________

Identify the terms, variables, coefficients, and constants in each expression.

3.

–4 a

– 7b

+ 5 + c 4. 7

– 5 h

– 2 – k

Terms: Terms:

Variables: Variables:

Coefficients:

Constants:

Coefficients:

Constants:

5. 5 – 4

Terms: x – 8y

Variables:

Coefficients:

Constants:

6. 9 k + 7

Terms:

Variables:

Constants: k

Coefficients:

+ 4

Inequality – a mathematical sentence that contains the symbols: ___ ___ ___ ___ .

>: _________________________

≥: _________________________

< : _____________________

≤ : _______________________

Tell whether the following phrases are expressions, equations, or inequalities. Circle the key symbol.

1) 5x > 25 2)

1

2 𝑥 – 2

3) 29 – k

7) –4m = 16

4) 8b + 9c < 45

5) 𝑥𝑦

12

6) r – (–12) = 9

8) h + (–9) ≥ 3

Write without parentheses (Simplify the expressions):

(–a)3

4(–b)

(–5)x

–(–8)y

(–1)(–c)

(–d)(–6)

–8(–m)

(–3)2x –3(2x) 3(–2x)

–n(–7)

–3(–2x)

(–3)6a

6a(2)

(–7x)(–5)

–6a(2)

–8m (3)

6a(–2)

–6(–2d)

(–6a)(–2)

Label the following parts.

Math

Sentence

3x – 2 = 16

Variables Coefficients Constants # of Terms

Equation,

Expression, or

Inequality?

Homework 3.1

1. Label the following parts.

Math

Sentence

5x = 40

Variables Coefficients Constants # of Terms

Equation,

Expression, or

Inequality?

12 + y > 13

3k – x + 9 w + (–6) = 7

–10 + 3x – x

2. Write without parentheses (Simplify the expressions):

4b(–8) –6(4y) –4(–3n)

14x(–7) 14x(–7) –14x(–7)

–7c(–3)

–14x(7)

Identify the terms, variables, coefficients, and constants in each expression.

3)

–5a – 7

+ 5d + h 4) 7m

– 5 – n – 8k

Terms: Terms:

Variables: Variables:

Coefficients: Coefficients:

Constants: Constants:

Tell whether the following phrases are expressions, equations, or inequalities. Circle the key symbol.

5) 5x = 25 – 3x

7) 29 – k ≥ -5

6)

1

2 𝑥 < 2

8) 8b + 9c + 45

9) A sentence containing the symbol < is called a(n) _________________.

10) Expressions that represent repeated multiplication are called __________________.

11) An integer and its opposite are _____________________________.

12) What is the multiplicative inverse of 5? _______

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