Solving Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

How do you solve the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

What does the solution x ≤ 8 represent on a number line?

Back

It represents all numbers less than or equal to 8, including 8 itself.

Front

What is the graph of the inequality 3x - 2y < 10?

Back

The graph is a region below the line 3x - 2y = 10, not including the line itself.

Front

What is the first step in solving a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane.

Front

What does the inequality y > 4x - 2 represent graphically?

Back

It represents the region above the line y = 4x - 2, not including the line.

Front

How do you determine if a point is a solution to an inequality?

Back

Substitute the point's coordinates into the inequality and check if the statement is true.

Front

What is the solution to the inequality -2x + 3 < 7?

Back

Subtract 3 from both sides: -2x < 4; then divide by -2 (reverse the inequality): x > -2.

Front

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

Back

It means 'less than or equal to'.

Front

What is the difference between '>' and '≥'?

Back

'>' means 'greater than' (not including the value), while '≥' means 'greater than or equal to' (including the value).