Compound Inequalities and Absolute value Equations

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more simple inequalities using the words 'and' or 'or'.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, isolate the variable in the middle and ensure the solution satisfies all parts of the inequality.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

What is the first step in solving an absolute value equation?

Back

The first step is to drop the absolute value bars by splitting the equation into two separate equations.

Front

How do you express the solution of an absolute value equation?

Back

The solution of an absolute value equation is expressed as 'x = a OR x = -a' if the equation is |x| = a.

Front

What is the solution to the inequality -3 ≤ 2x - 1 ≤ 5?

Back

The solution is -1 ≤ x ≤ 3.

Front

What does 'OR' mean in compound inequalities?

Back

'OR' means that at least one of the inequalities must be true for the solution to be valid.

Front

What does 'AND' mean in compound inequalities?

Back

'AND' means that both inequalities must be true for the solution to be valid.

Front

How do you graph a compound inequality with 'OR'?

Back

When graphing a compound inequality with 'OR', you shade the regions that satisfy either inequality.