Solving Equations and Inequalities

The video tutorial covers solving multi-step equations with variables on both sides, using the distributive property, and clearing fractions. It provides detailed solutions to two homework problems, emphasizing the importance of following systematic steps to simplify and solve equations. The tutorial also highlights common pitfalls, such as sign errors, and demonstrates how to verify solutions.

What is the first step in solving multi-step equations with variables on both sides?

• Add a constant to both sides

• Use the distributive property

• Clear fractions

• Combine like terms

When using the distributive property, what should you be careful about?

• The signs of the terms

• The constants on both sides

• The order of operations

• The coefficients of the variables

How do you decide which variable to move when solving equations with variables on both sides?

• Move the variable with the lower coefficient

• Move the variable with the positive coefficient

• Move the variable with the negative coefficient

• Move the variable with the higher coefficient

What is the next step after isolating the variable in a two-step equation?

• Add a constant to both sides

• Check the solution by substituting back into the original equation

• Use the distributive property again

• Multiply both sides by a fraction

What is the purpose of clearing fractions in an equation?

• To simplify the equation

• To eliminate variables

• To make the equation a one-step equation

• To change the signs of the terms

What is the least common denominator used for in solving equations with fractions?

• To multiply fractions

• To add fractions

• To subtract fractions

• To clear fractions

What happens when you multiply both sides of an equation by the same number?

• The constants are eliminated

• The variables are eliminated

• The equation becomes unbalanced

• The equation remains balanced

How do you handle a negative sign outside the parentheses?

• Subtract it from the terms inside

• Add it to the terms inside

• Distribute it across the terms inside

• Ignore it

What is the result of multiplying a negative number by another negative number?

• Zero

• A positive number

• A negative number

• The same negative number

What should you do after solving an equation to ensure your solution is correct?

• Divide the solution by a constant

• Multiply the solution by a constant

• Check the solution by substituting it back into the original equation

• Re-solve the equation