Solving Linear Inequalities: Key Concepts and Techniques

What is an inequality?

• An equation with only negative numbers

• An equation with a greater-than, less-than, greater-than or equal-to, or less-than or equal-to sign

• An equation with only positive numbers

• An equation with an equal sign

What is the first step in solving the inequality 2x + 3 <= 11?

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 2

• Divide both sides by 2

What is the solution to the inequality 2x + 3 <= 11?

• x <= 4

• x >= 4

• x <= 8

• x >= 8

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

• Keep the inequality sign the same

• Flip the direction of the inequality sign

• Subtract the same number from both sides

• Add the same number to both sides

What is the solution to the inequality -2x + 3 <= 11?

• x >= -4

• x >= 4

• x <= 4

• x <= -4

What is the first step in solving the inequality -1/2x + 4 > 7?

• Add 4 to both sides

• Subtract 4 from both sides

• Divide both sides by -2

• Multiply both sides by -2

What is the solution to the inequality -1/2x + 4 > 7?

• x < -6

• x > 6

• x > -6

• x < 6

What should you do if you encounter a fraction in a linear inequality?

• Divide both sides by the fraction

• Multiply both sides by the reciprocal of the fraction

• Subtract the fraction from both sides

• Add the fraction to both sides

When solving inequalities, when do you need to flip the inequality sign?

• When adding or subtracting a positive number

• When multiplying or dividing by a negative number

• When subtracting a negative number

• When adding a negative number

What is the key difference between solving a normal equation and an inequality?

• You need to flip the inequality sign when multiplying or dividing by a negative number

• There is no difference

• You need to add more steps in inequalities

• You need to use different operations