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 (such as <, >, ≤, or ≥).

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is strictly greater than the value on the right.

Front

How do you solve the inequality 3(x-2) < 2(x+9)?

Back

First, distribute: 3x - 6 < 2x + 18. Then, isolate x: 3x - 2x < 18 + 6, which simplifies to x < 24.

Front

What is the solution to the inequality 11h + 400 > 1200?

Back

To solve, subtract 400 from both sides: 11h > 800. Then, divide by 11: h > 72.73.

Front

Translate the phrase: 'Tom can spend no more than 20 dollars.'

Back

The inequality is t ≤ 20.

Front

What does 'at most' mean in terms of inequalities?

Back

'At most' indicates a maximum limit, represented by the symbol '≤'.

Front

What is the difference between '<' and '≤'?

Back

'<' means 'less than' (not including the value), while '≤' means 'less than or equal to' (including the value).

Front

What does the solution set of an inequality represent?

Back

The solution set represents all possible values that satisfy the inequality.

Front

How do you graph the inequality x < 24?

Back

Graph a number line, place an open circle at 24, and shade to the left to indicate all values less than 24.