Multistep Inequalities - solve, graph, identify solutions

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, or division.

Front

How do you solve the inequality -138 ≥ -6(6b − 7)?

Back

First, distribute -6: -138 ≥ -36b + 42. Then, subtract 42 from both sides: -180 ≥ -36b. Finally, divide by -36 (remember to flip the inequality): b ≥ 5.

Front

What does the solution x < 1 represent in a graph?

Back

It represents all the values to the left of 1 on a number line, not including 1 itself.

Front

How do you solve the inequality 3(y + 5) ≥ 21?

Back

First, distribute 3: 3y + 15 ≥ 21. Then, subtract 15 from both sides: 3y ≥ 6. Finally, divide by 3: y ≥ 2.

Front

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

Back

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

Front

What does the inequality x ≤ -11 mean?

Back

It means that x can be any number less than or equal to -11.

Front

How do you graph the solution x ≥ -7?

Back

Draw a number line, place a closed circle on -7, and shade to the right to indicate all numbers greater than or equal to -7.

Front

What is the first step in solving the inequality 2x - 3 < 7?

Back

Add 3 to both sides: 2x < 10.

Front

What does the term 'flipping the inequality' mean?

Back

It means reversing the direction of the inequality sign when multiplying or dividing by a negative number.

Front

How do you solve the inequality 4x + 8 ≥ 24?

Back

Subtract 8 from both sides: 4x ≥ 16. Then, divide by 4: x ≥ 4.