Solving Multistep Inequalities Challenge

The video tutorial covers solving multi-step linear inequalities. It begins with an introduction to the goal of isolating the variable and provides reminders about flipping the inequality sign when multiplying or dividing by a negative. The tutorial then walks through four examples, demonstrating how to simplify both sides, combine like terms, and graph the solutions on a number line. Each example highlights different techniques, such as distribution and variable movement, to solve inequalities effectively.

What is the primary goal when solving multi-step linear inequalities?

• To graph the solution

• To isolate the variable

• To find the value of the constant

• To simplify both sides

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

• Keep the inequality sign the same

• Add the same number to both sides

• Subtract the same number from both sides

• Flip the inequality sign

In the inequality 3x + 12 - 9x ≤ -9, what is the result of combining like terms on the left side?

• 6x + 12

• 6x - 12

• -6x + 12

• -6x - 12

After simplifying the inequality 3x + 12 - 9x ≤ -9, what is the next step?

• Add 12 to both sides

• Subtract 12 from both sides

• Multiply both sides by -6

• Divide both sides by -6

When graphing the solution x ≥ 7/2, what type of circle is used and in which direction does the arrow point?

• Closed circle, pointing left

• Open circle, pointing right

• Closed circle, pointing right

• Open circle, pointing left

In the inequality 5x - 7(x + 1) > -9, what is the result of distributing -7?

• 5x - 7x + 7

• 5x - 7x - 7

• 5x + 7x - 7

• 5x + 7x + 7

After simplifying the inequality 5x - 7(x + 1) > -9, what is the next step?

• Add 7 to both sides

• Subtract 7 from both sides

• Divide both sides by -2

• Multiply both sides by -2

In the inequality -3x - 3 ≥ 5 - 4x, what is the result of adding 4x to both sides?

• x + 3 ≥ 5

• -x + 3 ≥ 5

• -x - 3 ≥ 5

• x - 3 ≥ 5

After simplifying the inequality -3x - 3 ≥ 5 - 4x, what is the next step?

• Subtract 9 from both sides

• Subtract 3 from both sides

• Add 3 to both sides

• Add 9 to both sides

In the inequality 3(x + 1) - 9 < -2(x + 7) + 3x, what is the result of distributing -2?

• 2x - 14

• -2x - 14

• -2x + 14

• 2x + 14