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 operations such as addition, subtraction, multiplication, or division.

Front

How do you solve the inequality -8(m + 2) < 4(5 + 2m)?

Back

First, distribute: -8m - 16 < 20 + 8m. Then, combine like terms: -16 < 20 + 16m. Finally, isolate m: -36 < 16m, or m > -2.

Front

What does it mean if a value satisfies an inequality?

Back

It means that when the value is substituted into the inequality, the resulting statement is true.

Front

Does x + 9 > 21 hold true when x = 15?

Back

Yes, because 15 + 9 = 24, which is greater than 21.

Front

How do you isolate a variable in an inequality?

Back

Perform the same operations on both sides of the inequality to isolate the variable, just like in equations.

Front

What is the solution to the inequality a - 6 ≤ 15 + 8a?

Back

a ≥ -3, after rearranging the inequality.

Front

What is the solution set for the inequality 6 - 2h > 30?

Back

h < -12, after isolating h.

Front

What does the symbol '>' represent in inequalities?

Back

It indicates that the value on the left is greater than the value on the right.

Front

What is the first step in solving a multistep inequality?

Back

Identify and simplify both sides of the inequality if possible.

Front

What is the difference between '≥' and '>' in inequalities?

Back

'≥' means 'greater than or equal to', while '>' means 'greater than' only.