4.1-4.2 Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is greater than 5.

Front

How do you solve the inequality x + 3.5 ≤ 90?

Back

Subtract 3.5 from both sides: x ≤ 90 - 3.5, which simplifies to x ≤ 86.5.

Front

What is the solution set of the inequality x + y > -10 when x = -15?

Back

The solution set is y > 5.

Front

What does it mean for a number to be a solution of an inequality?

Back

A number is a solution of an inequality if it makes the inequality true when substituted into it.

Front

How can you check if -1 is a solution of the inequality 6w < -2?

Back

Substitute -1 for w: 6(-1) < -2, which simplifies to -6 < -2. This is true, so -1 is a solution.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 10 means x is less than or equal to 10.

Front

What is the graph of the inequality k > 1?

Back

The graph of k > 1 is a number line with an open circle at 1 and shading to the right.

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that can satisfy the inequality.