How do you solve the absolute value equation $$|\frac{x}{4}| = 8$$ ?

To solve $$|\frac{x}{4}| = 8$$ , set up two equations: $$\frac{x}{4} = 8$$ and $$\frac{x}{4} = -8$$ . Solving these gives $$x = 32$$ and $$x = -32$$ .

How do you solve the equation $$2x - 14 = 6$$ ?

To solve $$2x - 14 = 6$$ , add 14 to both sides to get $$2x = 20$$ , then divide by 2 to find $$x = 10$$ .

How do you solve the absolute value inequality $$|8x + 4| > 12$$ ?

To solve $$|8x + 4| > 12$$ , set up two inequalities: $$8x + 4 > 12$$ and $$8x + 4 1$$ or $$x

What is the solution set for the inequality $$|x|

The solution set for the inequality $$|x|

What is a linear equation?

A linear equation is an equation that represents a straight line when graphed. It can be written in the form $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

What does it mean for a system of equations to have infinitely many solutions?

A system of equations has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

How do you graph an inequality like $$y > 2x + 1$$ ?

To graph $$y > 2x + 1$$ , first graph the line $$y = 2x + 1$$ as a dashed line (since it's not inclusive), then shade the area above the line.

What is the slope-intercept form of a linear equation?

The slope-intercept form of a linear equation is $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

How do you find the x-intercept of a linear equation?

To find the x-intercept of a linear equation, set $$y = 0$$ and solve for $$x$$ .

What is the difference between an equation and an inequality?

An equation states that two expressions are equal, while an inequality shows the relationship between expressions that are not necessarily equal, using symbols like , ≤, or ≥.

What is a solution to an equation?

A solution to an equation is a value that, when substituted for the variable, makes the equation true.

How do you check if a solution is correct for an equation?

To check if a solution is correct, substitute the solution back into the original equation and verify if both sides are equal.

Solving Equations and Inequalities by graphing Flashcards

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1.

FLASHCARD QUESTION

Front

What is an absolute value equation?

Back

2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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What does it mean when a system of linear equations has no solutions?

Back

A system of linear equations has no solutions when the lines representing the equations are parallel and never intersect.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, indicating a range of values that satisfy the inequality.

6.

FLASHCARD QUESTION

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7.

FLASHCARD QUESTION

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