Solving Linear Inequalities with Decimals

This video tutorial covers Objective 16, focusing on solving linear inequalities with decimals. It extends previous lessons on inequalities by treating decimals like integers. Key rules include flipping the inequality when multiplying or dividing by a negative. The tutorial provides three examples: solving 0.7X > 3.5, -0.6X ≤ 7.2, and 5.4 > 1.2X - 0.6, demonstrating step-by-step solutions and graphing techniques.

What is the main difference when solving linear inequalities with decimals compared to integers?

• You need to convert them to fractions first.

• You need to use a different set of rules.

• You treat them the same as integers.

• You cannot solve them using a calculator.

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Keep the inequality sign the same.

• Flip the inequality sign.

• Subtract the same number from both sides.

• Add the same number to both sides.

In the inequality 0.7X > 3.5, what is the first step to isolate X?

• Add 0.7 to both sides.

• Multiply both sides by 0.7.

• Divide both sides by 0.7.

• Subtract 0.7 from both sides.

When graphing the solution to 0.7X > 3.5, what type of circle is used at 5?

• Shaded circle

• Open circle

• Closed circle

• No circle

In the inequality -0.6X ≤ 7.2, what must you do after dividing both sides by -0.6?

• Keep the inequality sign the same.

• Flip the inequality sign.

• Subtract 0.6 from both sides.

• Add 0.6 to both sides.

What is the solution to the inequality -0.6X ≤ 7.2 after dividing both sides by -0.6?

• X ≤ 12

• X ≥ 12

• X ≥ -12

• X ≤ -12

In the inequality 5.4 > 1.2X - 0.6, what is the first step to isolate X?

• Divide both sides by 1.2.

• Subtract 0.6 from both sides.

• Add 0.6 to both sides.

• Multiply both sides by 1.2.

After solving 5.4 > 1.2X - 0.6, what is the value of X?

• X > 5

• X ≥ 5

• X < 5

• X ≤ 5

When graphing the solution to 5.4 > 1.2X - 0.6, what type of circle is used at 5?

• No circle

• Shaded circle

• Open circle

• Closed circle

What direction do you shade when graphing the solution to 5.4 > 1.2X - 0.6?

• To the left

• Downwards

• To the right

• Upwards