What is the process to solve $$4p + 2a - 5 = 6a + p$$ ?

Rearranging gives $$4p - p = 6a - 2a + 5$$ , simplifying to $$3p = 4a + 5$$ , thus $$p = \frac{4a + 5}{3}$$ .

How do you solve $$4(x + 1) = 5x + 10$$ ?

Distributing gives $$4x + 4 = 5x + 10$$ . Rearranging leads to $$4 = x + 10$$ , thus $$x = -6$$ .

How do you solve $$6z = 49 - z$$ ?

Add $$z$$ to both sides to get $$7z = 49$$ , then divide by 7 to find $$z = 7$$ .

What is the importance of checking your solution in an equation?

Checking your solution ensures that it satisfies the original equation, confirming that no errors were made during the solving process.

What is the definition of a coefficient in an equation?

A coefficient is a numerical factor that multiplies a variable in an algebraic expression, such as the 7 in $$7x$$ .

What is the difference between an equation and an expression?

An equation states that two expressions are equal, while an expression is a combination of numbers, variables, and operators without an equality sign.

What does it mean to simplify an equation?

Simplifying an equation involves combining like terms and reducing it to its simplest form to make solving easier.

What is the first step in solving a linear equation?

The first step is to eliminate any constants from the side of the variable you are solving for, often by adding or subtracting.

What is the significance of the slope in a linear equation?

The slope indicates the steepness of the line and the direction it moves; a positive slope rises, while a negative slope falls.

Week 6 (PT): Solving Linear Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a linear equation?

Back

2.

FLASHCARD QUESTION

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How do you isolate a variable in an equation?

Back

3.

FLASHCARD QUESTION

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Back

4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

6.

FLASHCARD QUESTION

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Back

7.

FLASHCARD QUESTION

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