Solving Linear Inequalities in One Variable

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 −2x ≥ 16?

Back

Divide both sides by -2, remembering to flip the inequality sign: x ≤ -8.

Front

What does the solution x ≤ -8 represent on a number line?

Back

It represents all numbers less than or equal to -8, including -8 itself.

Front

How do you solve the inequality 4x + 3 ≤ −6?

Back

Subtract 3 from both sides: 4x ≤ -9. Then divide by 4: x ≤ -2.25.

Front

What is the solution to the inequality x + 8 > 11?

Back

Subtract 8 from both sides: x > 3.

Front

What does the solution x > 3 represent on a number line?

Back

It represents all numbers greater than 3, not including 3.

Front

How do you graph the inequality k < 3?

Back

Draw a number line, place an open circle at 3, and shade to the left.

Front

What is the difference between ≤ and < in inequalities?

Back

≤ includes the boundary value, while < does not.

Front

How do you solve the inequality 3x − 8 ≥ 4(x − 1.5)?

Back

Distribute and simplify: 3x - 8 ≥ 4x - 6. Then solve for x: x ≤ -2.

Front

What is the solution set for the inequality 2x + 5 < 13?

Back

Subtract 5 from both sides: 2x < 8. Then divide by 2: x < 4.