solving 2 step inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality 2x + 1 < -3?

Back

Subtract 1 from both sides to get 2x < -4, then divide by 2 to find x < -2.

Front

What does the solution f > -6 represent in terms of a number line?

Back

It represents all numbers greater than -6, which is shown as an open circle at -6 and a line extending to the right.

Front

How do you solve the inequality -24 + k ≤ 10?

Back

Add 24 to both sides to get k ≤ 34.

Front

What does the inequality 2x - 1 > 5 mean?

Back

It means that when you add 1 to both sides and then divide by 2, the solution is x > 3.

Front

What is the meaning of the compound inequality 6 >= x > -1?

Back

It means that x is less than or equal to 6 and greater than -1, which can be represented on a number line.

Front

What is the first step in solving a two-step inequality?

Back

The first step is usually to isolate the term with the variable by performing the inverse operation (addition or subtraction).

Front

How do you graph the solution of an inequality on a number line?

Back

Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.

Front

What is the difference between an open and closed interval in inequalities?

Back

An open interval does not include its endpoints (using < or >), while a closed interval includes its endpoints (using ≤ or ≥).

Front

How do you check your solution for a two-step inequality?

Back

Substitute the solution back into the original inequality to see if it makes the inequality true.