Solving Equations with Variables on Both Sides

This video tutorial guides viewers through solving equations with variables on both sides. It covers multiple examples, demonstrating different methods to solve equations, including those with fractions. The tutorial also addresses special cases like no solution and infinite solutions, providing a comprehensive understanding of the topic.

What is a constant in the context of an equation?

• A method of solving

• A type of equation

• A number that does not change

• A variable that can change

If you have variables and constants on both sides of an equation, which can you choose to eliminate first?

• Neither

• Either constants or variables

• Always variables

• Always constants

In the equation 5c = 7c - 10, what is a smart next step after simplifying?

• Subtract 7c from both sides

• Divide both sides by c

• Multiply both sides by c

• Add 5c to both sides

When solving for y in the equation 6y + 26 = 8y, what is the correct step to isolate y?

• None of the above

• Subtract 6y from both sides

• Subtract 8y from both sides

• Add 6y to both sides

How do you handle equations with fractions to simplify solving?

• Subtract the fractions

• Add the fractions

• Multiply by the least common denominator

• Ignore the fractions

What does it mean to distribute in the context of solving equations?

• Subtract terms

• Add terms

• Divide terms

• Multiply terms across a parenthesis

What is the purpose of subtracting 5/8x from both sides in the equation 1/2 - 5/8x = 7/8x + 7/2?

• All of the above

• To eliminate the x term

• To balance the equation

• To simplify the equation

What happens if you subtract a variable from both sides and are left with a false statement like 0 = 6?

• The equation has multiple solutions

• The equation has no solution

• The equation needs to be rechecked

• The equation is true for all numbers

What is the result when both sides of the equation simplify to the same number, like 12 = 12?

• Needs further simplification

• No solution

• One specific solution

• True for all real numbers

What should you do if an equation simplifies to 0 = 0?

• The equation has no solution

• Restart the problem

• The equation is incorrect

• The equation is true for all real numbers