Solving Equations and Inequalities

The video tutorial covers solving equations and inequalities. It begins with an introduction to equations, emphasizing the goal of isolating X. The tutorial demonstrates applying the distributive property and solving for X, followed by checking solutions. It then transitions to inequalities, explaining the differences from equations and the steps to solve them, including the importance of reversing inequality signs when multiplying or dividing by negative numbers. The tutorial concludes with verifying solutions to inequalities.

What is the first step in solving an equation with a distributive property?

• Multiply both sides by zero

• Subtract the smallest number

• Add all numbers on both sides

• Apply the distributive property

When simplifying an equation, what should you do after moving all variables to one side?

• Subtract or add numbers to isolate the variable

• Multiply by the variable

• Divide by zero

• Add 10 to both sides

Why is it important to check your solution after solving an equation?

• To make the equation more complex

• To ensure the solution satisfies the original equation

• To add more variables

• To change the variable

What is a key difference between solving equations and inequalities?

• You must reverse the inequality sign when multiplying or dividing by a negative number

• Inequalities have no solutions

• Inequalities require adding variables

• Equations always have more than one solution

When solving inequalities, what should you do if you multiply or divide by a negative number?

• Keep the inequality sign the same

• Reverse the inequality sign

• Add 5 to both sides

• Subtract 5 from both sides

How can you verify if a solution to an inequality is correct?

• By multiplying the solution by zero

• By adding the solution to both sides

• By checking if the solution satisfies the inequality

• By ignoring the inequality sign

What should you do if the inequality is 'x < -12' and you want to test a solution?

• Choose a number greater than -12

• Choose a number less than -12

• Choose any positive number

• Choose exactly -12

What is the result of dividing -14 by 2 when solving inequalities?

• 7

• -7

• 14

• -14

Why is it beneficial to choose even numbers when testing solutions for inequalities?

• They are easier to divide by 2

• They are always correct

• They make the inequality false

• They are larger than odd numbers

What is the final step after solving an inequality?

• Add the solution to both sides

• Multiply the solution by zero

• Ignore the solution

• Check the solution with different values