Solving 1 and 2 Step Inequalities

Dr. Metro explains how to solve one-step and two-step inequalities, highlighting the differences from solving equations. The video covers graphing inequalities on a number line, emphasizing the importance of directionality and infinite solutions. Special attention is given to the rules for multiplying or dividing by negative numbers, which require flipping the inequality symbol. Examples are provided to illustrate these concepts, ensuring a comprehensive understanding of solving inequalities.

What is an inequality?

• A sentence that involves only numbers.

• A sentence that involves different symbols than the equal sign.

• A sentence that involves only the equal sign.

• A sentence that involves only variables.

Which of the following is NOT a symbol used in inequalities?

• ≤

• >

• <

• =

When graphing the inequality x > -2, what should you do at -2 on the number line?

• Put a filled-in dot at -2.

• Put an open circle at -2.

• Put a filled-in dot at 0.

• Put an open circle at 0.

In the inequality x ≤ 4, which direction does the arrow point on the number line?

• Downwards

• Upwards

• To the left

• To the right

What happens to the inequality symbol when you multiply or divide both sides by a negative number?

• It disappears.

• It becomes an equal sign.

• It flips direction.

• It stays the same.

If you start with the inequality 8 < 10 and add 7 to both sides, what is the resulting inequality?

• 15 < 17

• 15 > 17

• 8 < 10

• 8 > 10

In the inequality G - 4 ≤ 15, what is the value of G after solving?

• G ≥ 19

• G ≥ 11

• G ≤ 19

• G ≤ 11

When graphing the solution to G - 4 ≤ 15, what should you do at 19 on the number line?

• Put an open circle at 19.

• Put a filled-in dot at 15.

• Put a filled-in dot at 19.

• Put an open circle at 15.

In the inequality -3M < 18, what is the value of M after solving?

• M > 6

• M < 6

• M > -6

• M < -6

When solving the two-step inequality -5M ≥ -25, what must you remember to do?

• Add 5 to both sides.

• Keep the inequality symbol the same.

• Subtract 5 from both sides.

• Flip the inequality symbol.