Solving Multi-Step Inequalities in Algebra

The video tutorial explains how to solve the inequality 5x + 7 > 3x + 1. It begins by simplifying the inequality through distribution and subtraction, then isolates x by dividing both sides. The solution, x > -2, is represented on a number line with an open circle at -2. The tutorial verifies the solution by testing values within and outside the solution set, confirming the correctness of the solution.

What is the first step in solving the inequality 5x + 7 > 3(x + 1)?

• Divide both sides by 5

• Add 3 to both sides

• Distribute the 3 on the right-hand side

• Subtract 7 from both sides

After distributing the 3 on the right-hand side, what does the inequality become?

• 5x + 7 > 3x + 3

• 5x + 7 > 3x + 1

• 5x + 7 > 3x + 4

• 5x + 7 > 3x + 7

What operation is performed to move the x terms to the left-hand side?

• Subtract 3x from both sides

• Add 3x to both sides

• Multiply both sides by 3

• Divide both sides by 3

What is the inequality after subtracting 3x from both sides?

• 2x + 7 > 3

• 2x + 7 > 7

• 2x + 7 > 0

• 2x + 7 > 4

What is the next step after obtaining 2x + 7 > 3?

• Add 7 to both sides

• Divide both sides by 2

• Subtract 7 from both sides

• Multiply both sides by 2

What is the inequality after subtracting 7 from both sides?

• 2x > -4

• 2x > 4

• 2x > -7

• 2x > 0

What is the final solution for x after dividing both sides by 2?

• x > -4

• x > -2

• x > 4

• x > 2

How is the solution x > -2 represented on a number line?

• A closed circle at -2 with shading to the right

• An open circle at -2 with shading to the right

• A closed circle at -2 with shading to the left

• An open circle at -2 with shading to the left

Which value should satisfy the inequality x > -2?

• -3

• 0

• -2

• -4

Which value should NOT satisfy the inequality x > -2?

• 0

• 1

• -1

• -3