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 (>, <, ≥, ≤).

Front

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

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). Then shade the region that satisfies the inequality.

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.

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 to the left of 8, including 8 itself.

Front

Which point is NOT a solution to the inequality y ≥ -3/4 x + 3?

Back

(5, 10) is NOT a solution because it does not satisfy the inequality.

Front

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

Back

'>' means greater than, while '≥' means greater than or equal to. The latter includes the boundary value.

Front

How can you check if a point is a solution to an inequality?

Back

Substitute the point's coordinates into the inequality. If the inequality holds true, the point is a solution.

Front

What does the graph of y < 4x - 2 look like?

Back

It is a dashed line representing the equation y = 4x - 2, with the area below the line shaded.