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

How do you solve the inequality -3 ≥ x - 1?

Back

Add 1 to both sides: -3 + 1 ≥ x, which simplifies to -2 ≥ x.

Front

What does the inequality 10 ≥ x - 3 represent?

Back

It represents that x can be at most 13, since adding 3 to both sides gives x ≤ 13.

Front

What is the solution to the inequality 15 > -5 + z?

Back

Add 5 to both sides: 20 > z, which can be rewritten as z < 20.

Front

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

Back

Subtract 5 from both sides: x ≤ 8.

Front

What does the inequality 7n > 49 imply about n?

Back

Divide both sides by 7: n > 7.

Front

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

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

What is the first step in solving a linear inequality?

Back

Isolate the variable on one side of the inequality.

Front

How do you graph the solution of an inequality like x ≤ 8?

Back

Draw a number line, shade to the left of 8, and use a closed circle at 8.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips direction.