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 (>, <, ≥, ≤) instead of an equal sign.

Front

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

Back

'≥' 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

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

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you solve the inequality 12 ≥ 15 - 6y?

Back

Rearranging gives 6y ≥ 3, which simplifies to y ≥ ½.

Front

What is the solution to the inequality 4(2a + 3) < 3(a - 1)?

Back

The solution is a < -3.

Front

How do you solve the inequality 6x + 10 > 5x - 12?

Back

Rearranging gives x > -22.

Front

What does the solution x ≤ 14 represent on a number line?

Back

It represents all values of x that are less than or equal to 14, including 14 itself.

Front

What does the solution x < -4 represent on a number line?

Back

It represents all values of x that are less than -4, not including -4.

Front

What is the first step in solving a linear inequality?

Back

The first step is to isolate the variable on one side of the inequality.

Front

What is the importance of checking your solution set in inequalities?

Back

Checking the solution set ensures that the values satisfy the original inequality and helps identify any errors.