How do you solve $$-9 - 3x = -2(x + 6)$$ ?

First, distribute and combine like terms: $$-9 - 3x = -2x - 12$$ . Then isolate $$x$$ to find $$x = 3$$ .

What is the first step in solving $$\frac{| -6n - 7 |}{9} = 2$$ ?

Multiply both sides by 9 to eliminate the fraction: $$| -6n - 7 | = 18$$ .

How do you solve $$5|x + 5| = 45$$ ?

Divide both sides by 5 to get $$|x + 5| = 9$$ . Then set up two equations: $$x + 5 = 9$$ and $$x + 5 = -9$$ .

What does $$|\frac{x}{2}| = 2$$ represent?

This represents two cases: $$\frac{x}{2} = 2$$ and $$\frac{x}{2} = -2$$ . Solve each case to find $$x = 4$$ and $$x = -4$$ .

How do you solve the inequality $$-147 > 3(8x + 7)$$ ?

Distribute and simplify: $$-147 > 24x + 21$$ . Then isolate $$x$$ to find $$x

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

What is a solution to an absolute value inequality?

A solution to an absolute value inequality is a range of values that satisfy the inequality, often expressed in interval notation.

What is the importance of checking solutions in inequalities?

Checking solutions in inequalities is important to ensure that the solution set does not include extraneous solutions that do not satisfy the original inequality.

Solving Linear and Absolute Value Equations and Inequalities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a linear equation?

Back

2.

FLASHCARD QUESTION

Front

What is an absolute value equation?

Back

3.

FLASHCARD QUESTION

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

4.

FLASHCARD QUESTION

Front

What does it mean to solve an absolute value equation?

Back

To solve an absolute value equation, you set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

5.

FLASHCARD QUESTION

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true. It can be represented on a number line.

6.

FLASHCARD QUESTION

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then shade the region that satisfies the inequality.

7.

FLASHCARD QUESTION

Front

What is the difference between strict and non-strict inequalities?

Back

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