Example: Isolating a variable

For the equation $$2x + 3 = 7$$ , subtract 3 from both sides to isolate $$2x$$ .

Definition: Linear Equation

An equation that makes a straight line when graphed, typically in the form $$y = mx + b$$ .

Example: Solving for a variable in a linear equation

For $$y = 2x + 5$$ , to solve for $$x$$ , rearrange to $$x = \frac{y - 5}{2}$$ .

Definition: Quadratic Equation

An equation of the form $$ax^2 + bx + c = 0$$ , where a, b, and c are constants.

Example: Solving a quadratic equation

Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

Definition: Proportional Relationships

Two quantities are proportional if they maintain a constant ratio.

Example: Solving for a variable in a proportion

If $$\frac{a}{b} = \frac{c}{d}$$ , then $$ad = bc$$ .

Definition: Function Notation

A way to represent a function using symbols, typically written as $$f(x)$$ .

Example: Evaluating a function

For $$f(x) = 2x + 3$$ , to find $$f(2)$$ , substitute 2 for x: $$f(2) = 2(2) + 3 = 7$$ .

Manipulating Equations Flashcards

Student preview

16 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

Solve for R: Q + R = H

Back

R = H - Q

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Solve for y: 3x + y = 12

Back

y = -3x + 12

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Definition: Manipulating Equations

Back

The process of rearranging an equation to isolate a specific variable.

7.

FLASHCARD QUESTION

Front

Principle: Inverse Operations

Back

To isolate a variable, perform the inverse operation of what is currently applied to it.

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