Solving MultiStep Inequalities

Front

What is a multi-step inequality?

Back

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: 9 ≥ -2m + 2 − 3?

Back

First, simplify: 9 ≥ -2m - 1. Then, add 1 to both sides: 10 ≥ -2m. Finally, divide by -2 (remember to flip the inequality): m ≥ -5.

Front

What does the solution m ≥ -5 represent on a number line?

Back

It represents all numbers greater than or equal to -5, including -5 itself.

Front

What is the first step in solving the inequality: -3 − 6(4x + 6) > -111?

Back

Distribute -6: -3 - 24x - 36 > -111.

Front

What is the solution to the inequality: 6x + 2 + 6x < 14?

Back

Combine like terms: 12x + 2 < 14. Then, subtract 2: 12x < 12. Finally, divide by 12: x < 1.

Front

What does the inequality 6 > x mean?

Back

It means that x can be any number less than 6.

Front

How do you represent a taxi fare scenario as an inequality?

Back

If the fare is $2.50 per mile plus a $5 fee, the inequality is 2.50x + 5 ≤ 20, where x is the number of miles.

Front

What is the importance of flipping the inequality sign when multiplying or dividing by a negative number?

Back

Flipping the sign ensures that the inequality remains true, as multiplying or dividing by a negative reverses the order.

Front

What is the solution to the inequality: 2.50x + 5 ≤ 20?

Back

Subtract 5 from both sides: 2.50x ≤ 15. Then, divide by 2.50: x ≤ 6.

Front

What does the term 'isolating the variable' mean in solving inequalities?

Back

It means to manipulate the inequality so that the variable is on one side and all other terms are on the opposite side.