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 6x + 2 < 14?

Back

Subtract 2 from both sides: 6x < 12. Then divide by 6: x < 2.

Front

What is the solution to the inequality -3 − 6(4x + 6) > -111?

Back

First, distribute: -3 - 24x - 36 > -111. Combine like terms: -24x > -72. Divide by -24 (remember to flip the inequality): x < 3.

Front

What does the solution x ≥ -7 represent?

Back

It means that x can be any number greater than or equal to -7.

Front

How do you write the solution x < 8 in interval notation?

Back

(-∞, 8) represents all numbers less than 8.

Front

What is the first step in solving the inequality -138 ≥ -6(6b − 7)?

Back

Distribute -6: -138 ≥ -36b + 42.

Front

What does the inequality b ≥ 5 mean?

Back

It means that b can be any number greater than or equal to 5.

Front

How do you isolate the variable in the inequality 2x + 3 < 11?

Back

Subtract 3 from both sides: 2x < 8, then divide by 2: x < 4.

Front

What is the solution to the inequality 5x - 2 > 3x + 6?

Back

Subtract 3x from both sides: 2x - 2 > 6. Then add 2: 2x > 8. Finally, divide by 2: x > 4.

Front

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

Back

Flipping the inequality sign ensures that the relationship between the two sides of the inequality remains true.