Unit 2 Extra Credit

Front

What is the absolute value of a number?

Back

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

Front

How do you solve an equation involving absolute value, such as |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there are no values that can satisfy the equation, often due to contradictory statements.

Front

What is the solution to the equation |n + 5| = 21?

Back

The solutions are n = 16 and n = -26.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation p + 3.4 = 8.7?

Back

Subtract 3.4 from both sides to isolate p.

Front

What is the solution to the equation p + 3.4 = 8.7?

Back

p = 5.3.

Front

What is the definition of a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What does the term 'no solution' indicate in the context of absolute value equations?

Back

It indicates that the equation cannot be satisfied by any real number.

Front

How do you determine if an absolute value equation has one solution, two solutions, or no solutions?

Back

Analyze the equation: if the expression inside the absolute value can equal the positive and negative of the other side, it has two solutions; if it can only equal one, it has one solution; if it leads to a contradiction, it has no solution.