Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 3 < -5n + 2n?

Back

Combine like terms to get 3 < -3n, then divide by -3 (remember to flip the inequality sign) to find n < -1.

Front

What does the solution x < 1 represent in a graph?

Back

It represents all values to the left of 1 on a number line, not including 1 itself.

Front

What is the first step in solving the inequality 6x + 2 < 14?

Back

Subtract 2 from both sides to simplify the inequality to 6x < 12.

Front

What is the solution to the inequality 9 ≥ -2m + 2 - 3?

Back

First simplify to 9 ≥ -2m - 1, then add 1 to both sides to get 10 ≥ -2m, and finally divide by -2 to find m ≥ -5.

Front

What does an infinite solution mean in the context of inequalities?

Back

It means that there are countless values that satisfy the inequality, often occurring when both sides of the inequality simplify to the same expression.

Front

How do you interpret the inequality -3 - 6(4x + 6) > -111?

Back

First, distribute -6 to get -3 - 24x - 36 > -111, then combine like terms and solve for x.

Front

What is the significance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign is necessary to maintain the truth of the inequality when multiplying or dividing by a negative number.

Front

What does the solution x > 3 indicate?

Back

It indicates that x can take any value greater than 3, not including 3 itself.

Front

What is the process of isolating the variable in an inequality?

Back

Isolating the variable involves performing operations to get the variable on one side of the inequality and the constant on the other.