Solving Inequalities with Negative Coefficients

The video tutorial explains how to solve inequalities in one variable with negative coefficients by dividing by a negative number and changing the direction of the inequality sign. It covers the process of checking solutions and provides examples to illustrate the method. The tutorial emphasizes the importance of reversing the inequality sign when multiplying or dividing by a negative number.

What must you do to the inequality sign when you divide both sides of an inequality by a negative number?

• Keep the sign the same

• Change the sign to an equal sign

• Reverse the direction of the sign

• Multiply the sign by negative one

In the inequality -5x + 7 ≥ 12, what is the first step to isolate x?

• Divide both sides by 7

• Multiply both sides by 5

• Subtract 7 from both sides

• Add 5 to both sides

After solving the inequality -5x + 7 ≥ 12, what is the correct solution for x?

• x ≤ 1

• x ≥ 1

• x ≤ -1

• x ≥ -1

When solving the inequality 10 - 3x > 37, what is the new inequality after taking the opposite of every term?

• -10 - 3x < 37

• 10 - 3x < -37

• 10 + 3x < 37

• -10 + 3x < -37

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

• x < 9

• x > 9

• x < -9

• x > -9