Solving Simple Equations with Distribution and Variables

The video tutorial provides a comprehensive review of solving simple equations, starting with two-step equations involving fraction coefficients. It explains the use of inverse operations to eliminate constants and the application of reciprocals to simplify equations. The tutorial also covers distribution in equations, demonstrating how to handle terms within parentheses. Finally, it addresses more complex equations with variables on both sides, emphasizing the importance of maintaining equality and using efficient methods to solve them.

What is the first step in solving a two-step equation with a subtraction constant?

• Subtract the constant from both sides

• Add the constant to both sides

• Divide both sides by the constant

• Multiply both sides by the constant

What does the reciprocal of a fraction represent?

• A fraction that when added to the original equals one

• A fraction that when multiplied by the original equals one

• A fraction that when subtracted from the original equals one

• A fraction that when multiplied by the original equals zero

How do you eliminate a fractional coefficient from an equation?

• Multiply both sides by the reciprocal

• Subtract the reciprocal from both sides

• Add the reciprocal to both sides

• Divide both sides by the reciprocal

What is the result of distributing 3 to (4 - x)?

• 12 + 3x

• 12 - 3x

• 7 + x

• 7 - x

How do you solve for x when dealing with a negative coefficient?

• Subtract the coefficient from both sides

• Divide both sides by the negative of the coefficient

• Add the coefficient to both sides

• Multiply both sides by the negative of the coefficient

What is the purpose of subtracting 8 from both sides in the equation 12x + 8 = 32?

• All of the above

• To simplify the constants

• To balance the equation

• To isolate the variable term on one side

What does distributing 7 to (2x - 1) result in?

• 9x - 1

• 9x + 1

• 14x + 7

• 14x - 7

When solving equations with variables on both sides, what is a common first step?

• Eliminate one variable term

• Distribute coefficients

• Isolate constants on one side

• Combine like terms

How do you handle negative coefficients when solving equations?

• Convert them to positive by multiplying

• Convert them to positive by dividing

• Convert them to positive by adding

• Convert them to positive by subtracting

What is the final step in solving the equation 3x - 7 = -22?

• Multiply both sides by 3

• Subtract 7 from both sides

• Divide both sides by 3

• Add 7 to both sides