Solving Inequalities with Negative Coefficients

The video tutorial teaches how to solve inequalities in one variable with negative coefficients by rewriting them to have positive coefficients. It explains the process using example problems, demonstrating how to manipulate the inequality and verify the solution by substitution. The tutorial also covers graphing the solution on a number line and provides a second example to reinforce the concept.

What is the first step in solving an inequality with a negative coefficient?

• Multiply both sides by a negative number

• Add or subtract terms to isolate the variable

• Switch the inequality sign

• Divide both sides by the coefficient

In the example where the inequality is -5x + 7 ≥ 12, what is the inequality after subtracting 7 from both sides?

• 5x ≤ 5

• 5x ≥ 5

• -5x ≤ 5

• -5x ≥ 5

How do you rewrite the inequality -5x ≥ 5 to have a positive coefficient?

• Divide both sides by -5

• Subtract 5x from both sides

• Add 5x to both sides

• Multiply both sides by -1

In the second example, what is the inequality after adding 3x to both sides of 10 - 3x > 37?

• 10 < 37 + 3x

• 10 = 37 + 3x

• 10 ≥ 37 + 3x

• 10 > 37 + 3x

What is the final solution for the inequality 10 - 3x > 37 after solving it?

• x ≥ -9

• x > -9

• x < -9

• x ≤ -9