Solving MultiStep Inequalities

Front

What is a multi-step inequality?

Back

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

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a specified number.

Front

How do you solve the inequality: 9 ≥ -2m + 2 - 3?

Back

First, simplify the right side: 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 an open endpoint on a number line indicate?

Back

An open endpoint indicates that the value at that point is not included in the solution set, typically used with '<' or '>'.

Front

What does a closed endpoint on a number line indicate?

Back

A closed endpoint indicates that the value at that point is included in the solution set, typically used with '≤' or '≥'.

Front

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

Back

The solution is 'infinitely many solutions' because the inequality simplifies to 2 < 14, which is always true.

Front

What is the first step in solving the inequality 2x + 3(3x - 2) ≥ 15x - 1 - 4x?

Back

Distribute the 3: 2x + 9x - 6 ≥ 15x - 1 - 4x.

Front

What does the inequality x > 3 represent on a number line?

Back

It represents all values of x that are greater than 3, with an open circle at 3 and shading to the right.

Front

What is the solution to the inequality 2x + 3(3x - 2) ≥ 15x - 1 - 4x?

Back

The solution is 'no solution' because the inequality simplifies to a false statement.

Front

What is the difference between 'no solution' and 'infinitely many solutions' in inequalities?

Back

'No solution' means there are no values that satisfy the inequality, while 'infinitely many solutions' means there are countless values that satisfy it.