Solving Linear Inequalities and Graphs

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 a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, typically shown as a shaded region on one side of a boundary line.

Front

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

Back

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

Front

What does the solution to the inequality 4x + 1 < -27 look like?

Back

To solve, subtract 1 from both sides: 4x < -28, then divide by 4: x < -7. The graph would show a line at -7 with shading to the left.

Front

How do you represent 'A number is greater than 2' as an inequality?

Back

It can be represented as x > 2.

Front

What does the graph of x > 5 look like?

Back

The graph has an open circle at 5 and shading to the right, indicating all numbers greater than 5.

Front

How do you solve the inequality -2x ≤ 16?

Back

Divide both sides by -2 (remember to reverse the inequality): x ≥ -8.

Front

What does the inequality x ≤ 7 represent?

Back

It represents all numbers less than or equal to 7, shown with a closed circle at 7 and shading to the left.

Front

What is the significance of an open circle on a graph?

Back

An open circle indicates that the number at that point is not included in the solution set (e.g., for x > 5).