Solving two step inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 21 = 9x + 3?

Back

To solve for x, first subtract 3 from both sides to get 18 = 9x, then divide both sides by 9 to find x = 2.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

How do you solve the inequality -3x ≥ 12?

Back

To solve for x, divide both sides by -3, which requires flipping the inequality sign, resulting in x ≤ -4.

Front

What is the solution to the inequality 7k - 2 ≥ -9?

Back

To solve for k, add 2 to both sides to get 7k ≥ -7, then divide by 7 to find k ≥ -1.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations (addition, subtraction, multiplication, division) while maintaining the direction of the inequality, unless dividing by a negative number.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

To solve for x, subtract 14 from both sides to get -4x ≤ 40, then divide by -4, flipping the inequality sign to find x ≥ -10.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality is shown on a number line, where a closed dot indicates inclusion (≤ or ≥) and an open dot indicates exclusion (< or >).

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if the variable cannot satisfy the inequality under any circumstances, such as when the inequality simplifies to a false statement like 0 < -1.