Solving Equations and Inequalities

The video tutorial covers solving equations with variables on both sides, focusing on rational coefficients. It explains how to balance equations by moving constants and variables, solve equations with fractions and decimals, and verify solutions. The tutorial emphasizes getting variables on one side and constants on the other to solve equations effectively.

What is a rational coefficient?

• A fraction or integer next to a variable

• A whole number

• A decimal number

• A number that is not next to a variable

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

• Divide both sides by a variable

• Multiply both sides by a constant

• Subtract all constants from both sides

• Add all variables to one side

How do you eliminate a fraction when solving an equation?

• Divide by the fraction

• Add the fraction to both sides

• Multiply by the reciprocal of the fraction

• Subtract the fraction from both sides

What is the solution to the equation 2/3x = 2?

• x = 1

• x = 2

• x = 3

• x = 4

When solving equations with decimals, what is a useful strategy?

• Convert decimals to fractions

• Ignore the decimals

• Add decimals to both sides

• Work with positive numbers

What is the solution to the equation 1.5x = -6?

• x = 3

• x = 4

• x = -3

• x = -4

How do you verify the solution of an equation?

• By asking a friend

• By using a calculator

• By solving the equation again

• By checking if the solution satisfies the original equation

What should you do if you have variables on both sides of an equation?

• Add them together

• Move them to one side

• Ignore them

• Multiply them by a constant

What is the final step in solving an equation?

• Subtract the smallest number

• Divide by the largest number

• Check the solution by plugging it back into the equation

• Add all numbers together

What is the solution to the equation 3x = 9?

• x = 1

• x = 2

• x = 3

• x = 4