Algebra 1 - Linear Equations Review

Questions and Answers

What is the first step to solving an equation?

distributive property

What is the second step to solving an equation?

Combining like terms on the SAME side of the equal sign

What is the third step to solving an equation?

undo inverse operations

What is a term in algebra?

A single number or variable (separated by - or +) Signup and view all the answers

What is a variable?

A letter or symbol for a number we don't know yet Signup and view all the answers

What is a coefficient?

A number used to multiply a variable (ex: 3x--> 3, z--> 1) Signup and view all the answers

What is a constant?

A fixed value (a number on its own) Signup and view all the answers

How many terms are there in the expression -4x - 2 + 1x³ - 7z² + 5 - 6z?

6 Signup and view all the answers

What are the coefficients in the expression -4x - 2 + 1x³ - 7z² + 5 - 6z?

-4, 1, -7, -6 Signup and view all the answers

What are the constants in the expression -4x - 2 + 1x³ - 7z² + 5 - 6z?

-2, 5 Signup and view all the answers

What are the variables in the expression -4x - 2 + 1x³ - 7z² + 5 - 6z?

x, x³, z², z Signup and view all the answers

What are like terms?

Terms whose variables (and exponents) are the same Signup and view all the answers

What is the inverse of addition?

Subtraction Signup and view all the answers

What is the inverse of subtraction?

Addition Signup and view all the answers

What is the inverse of multiplication?

Division Signup and view all the answers

What is the inverse of division?

Multiplication Signup and view all the answers

What is another word for addition?

Sum Signup and view all the answers

What is another word for subtraction?

Difference Signup and view all the answers

What is another word for multiplication?

Product Signup and view all the answers

What is another word for division?

Quotient Signup and view all the answers

What is the expression for the difference between three times a number and 4?

3x - 4 Signup and view all the answers

What is the expression for the quotient of a number and 4?

x ÷ 4 Signup and view all the answers

What is the expression for 25 increased by a number?

25 + x Signup and view all the answers

What is the expression for three less than a number y?

y - 3 Signup and view all the answers

What is the expression for three-fourths of a number m?

¾m Signup and view all the answers

How would you express that Mary has twice as many CDs as Lisa?

2x Signup and view all the answers

If I have already spent $30 at the mall and plan to buy 3 shirts that cost the same amount, how would I write the expression?

3x + 30 Signup and view all the answers

What is combining like terms?

A way you can simplify an algebraic expression that have the same variable and exponents Signup and view all the answers

What does the Distributive Property entail?

The number on the outside of the parenthesis is distributed to all the terms inside the parenthesis using multiplication Signup and view all the answers

Simplify the expression: -f + 3 - 4f + 8 - 2

-5f + 9 Signup and view all the answers

Simplify the expression: -8y + (-9y) + 3x + 5yx

-17y + 3x + 5yx Signup and view all the answers

Simplify the expression: 2x² - 3x + x² - 4x + 8

3x² - 7x + 8 Signup and view all the answers

Simplify using the Distributive Property: 5(3x - 4)

15x - 20 Signup and view all the answers

Simplify using the Distributive Property: -3(2h - 4)

-6h + 12 Signup and view all the answers

Simplify using the Distributive Property: 3(x + 2 - 5y)

3x + 6 - 15y Signup and view all the answers

What will you end up with if you have one solution to an equation?

x = ____ (The variable equal to a single number) Signup and view all the answers

What will you end up with if you have no solution to an equation?

0≠1 (Not a true statement) Signup and view all the answers

What will you end up with if you have infinite solutions to an equation?

0=0 (A true statement) Signup and view all the answers

In the equation y = mx + b, what does m represent?

slope / 'per' Signup and view all the answers

In the equation y = mx + b, what does b represent?

y-intercept / start value Signup and view all the answers

When performing inverse operations, what comes first?

Addition and Subtraction Signup and view all the answers

When performing inverse operations, what comes last?

Multiplication and Division Signup and view all the answers

Write an equation for the given situation: At one store a trophy costs $12, engraving costs $0.50 per letter.

y = 0.50x + 12 Signup and view all the answers

Write an equation for the given situation: A full 355ml of sprite is leaking at a rate of 5ml per minute.

y = -5x + 355 Signup and view all the answers

Study Notes

Solving Linear Equations

First step involves using the distributive property for expressions with parentheses.
Combining like terms occurs on the same side of the equation to simplify it further.
Lastly, undo inverse operations to isolate the variable.

Key Algebraic Concepts

Term: A single number or variable, separated by addition or subtraction.
Variable: Symbol (usually a letter) representing an unknown number.
Coefficient: A number multiplying a variable (e.g., in 3x, 3 is the coefficient).
Constant: A fixed value that stands alone in an expression.

Expression Analysis

In the expression -4x - 2 + 1x³ - 7z² + 5 - 6z, there are six terms total.
The coefficients in this expression are -4, 1, -7, -6.
The constants present are -2, 5.
Variables included in the expression are x, x³, z², z.

Understanding Like Terms

Like terms share the same variable and exponent. For example: 3x and 2x are like terms.

Inverse Operations

Inverse of addition is subtraction.
Inverse of subtraction is addition.
Inverse of multiplication is division.
Inverse of division is multiplication.

Alternative Terms for Operations

Addition can also be referred to as sum.
Subtraction is known as difference.
Multiplication is termed as product.
Division is called quotient.

Writing Algebraic Expressions

The expression for "the difference between three times a number and 4" is 3x - 4.
"The quotient of a number and 4" is represented as x ÷ 4.
"25 increased by a number" translates to 25 + x.
"Three less than a number y" can be expressed as y - 3.
"Three-fourths of a number m" is indicated by ¾m.

Expressions Based on Scenarios

If Mary has twice as many CDs as Lisa, it is represented by 2x.
Spending $30 at the mall and planning to buy 3 shirts is expressed as 3x + 30.

Combining Like Terms and Simplifying

Simplifying expressions involves combining like terms to rewrite them in a simpler form.

Distributive Property Application

The distributive property allows distributing multiplication over addition or subtraction in expressions.

Outcomes of Equations

A single solution results in x = ___ (specific value).
No solution yields a false statement: 0 ≠ 1.
Infinite solutions present a true statement: 0 = 0.

The Slope-Intercept Form

In the equation y = mx + b, m signifies the slope and b denotes the y-intercept or start value.

Order of Operations in Inverses

Addition and subtraction operations are performed first when solving equations.
Multiplication and division are done last in the process.

Writing Situational Equations

Cost of a trophy and engraving can be written as: y = 0.50x + 12.
The leaking sprite scenario can be modeled by the equation: y = -5x + 355.

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Description

Prepare for your Algebra 1 test on linear equations with this flashcard review. Learn essential steps such as using the distributive property, combining like terms, and applying inverse operations. Boost your understanding and confidence in solving equations effectively.