2 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 -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What does the solution x < 6 represent on a number line?

Back

It represents all numbers to the left of 6, not including 6 itself.

Front

How do you graph the inequality 7n - 1 > 76?

Back

First, solve for n: 7n > 77, then n > 11. Graph by shading to the right of 11, with an open circle at 11.

Front

What is the solution to the inequality -2x - 3 ≤ 13?

Back

Add 3 to both sides: -2x ≤ 16. Then divide by -2 (flip the inequality): x ≥ -8.

Front

How do you interpret the inequality 11 > -3y + 2?

Back

Rearranging gives -3y < 9, which simplifies to y > -3.

Front

What is the difference between an inequality and an equation?

Back

An inequality shows a relationship where one side is not necessarily equal to the other, while an equation states that two expressions are equal.

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

What is the solution set for the inequality x + 5 < 10?

Back

Subtract 5 from both sides: x < 5.

Front

How do you solve the inequality 3x - 4 ≥ 5?

Back

Add 4 to both sides: 3x ≥ 9, then divide by 3: x ≥ 3.