Solving Linear Inequalities

The video tutorial provides a comprehensive overview of inequalities, starting with a review of inequality symbols and their meanings. It explains how to solve linear inequalities using similar processes as solving equations, and how to represent solutions on a number line. The tutorial also covers solving simultaneous inequalities by breaking them into separate problems and finding a range of values. The session concludes with a summary of key points and a brief mention of dealing with negative coefficients in future lessons.

Which symbol represents 'less than or equal to'?

• <

• >

• ≥

• ≤

What is the first step in solving the inequality 3 ≤ 4x + 19?

• Add 19 to both sides

• Subtract 19 from both sides

• Divide by 4

• Multiply by 4

How do you represent the solution x ≥ -4 on a number line?

• Open circle at -4, arrow to the left

• Shaded circle at -4, arrow to the right

• Open circle at -4, arrow to the right

• Shaded circle at -4, arrow to the left

When solving 3x < 5x + 1 and 5x + 1 ≤ 2x + 9 simultaneously, what is the first step?

• Combine the inequalities

• Solve each inequality separately

• Subtract the inequalities

• Add the inequalities

What is the range of x for the inequalities 3x < 5x + 1 and 5x + 1 ≤ 2x + 9?

• x > -1/2 and x ≤ 8/3

• x ≤ -1/2 and x > 8/3

• x < -1/2 and x ≥ 8/3

• x ≥ -1/2 and x < 8/3

What should you do when you encounter negative coefficients while solving inequalities?

• Ignore them

• Reverse the inequality sign

• Add them to both sides

• Multiply them by zero

What is a key takeaway about solving inequalities?

• They cannot be represented on a number line

• They provide a range of values

• They provide a single value solution

• They use different processes than equations