Two-Step Inequality

Front

What is a two-step inequality?

Back

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

Front

How do you solve the inequality u/7 – 1 ≤ 1?

Back

Add 1 to both sides: u/7 ≤ 2. Then multiply both sides by 7: u ≤ 14.

Front

What is the solution to the inequality -n + 8 < 26?

Back

Subtract 8 from both sides: -n < 18. Then multiply by -1 (reversing the inequality): n > -18.

Front

Solve the inequality 2 - 3x ≤ 20.

Back

Subtract 2 from both sides: -3x ≤ 18. Then divide by -3 (reversing the inequality): x ≥ -6.

Front

What does the inequality -9a - 1 < 26 represent?

Back

It represents a condition where the expression on the left is less than 26. To solve, add 1 to both sides: -9a < 27, then divide by -9 (reversing the inequality): a > -3.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by performing the opposite operation (addition or subtraction) on both sides.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign reverses direction when you multiply or divide both sides of the 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 graph the solution of the inequality a > -3?

Back

You would draw a number line, place an open circle at -3, and shade to the right to indicate all numbers greater than -3.

Front

What is the difference between ≤ and < in inequalities?

Back

The symbol ≤ means 'less than or equal to', while < means 'less than' only, excluding the endpoint.