Solving Linear Equations Concepts

This video tutorial covers solving equations with one solution, no solution, and infinite solutions. It begins with a linear equation example that has one solution, demonstrating the steps to isolate the variable. The tutorial then explains how to identify equations with no solution, where the equation results in a false statement. Finally, it discusses equations with infinite solutions, where any value for the variable satisfies the equation. The video aims to help learners understand different types of solutions in equations.

What is the first step in solving a one-variable linear equation?

• Combine like terms

• Add constants to both sides

• Subtract variables from both sides

• Distribute any coefficients

In the equation 3(x + 3) - 27 = 4x - 36, what is the result after distributing the 3?

• 3x + 3 - 36

• 3x + 9 - 36

• 3x + 3 - 27

• 3x + 9 - 27

After combining like terms in the equation 3x + 9 - 27 = 4x - 36, what is the simplified form?

• 3x + 8 = 4x - 36

• 3x - 8 = 4x - 36

• 3x - 8 = 4x + 36

• 3x - 18 = 4x - 36

What is the next step after simplifying the equation to 3x - 8 = 4x - 36?

• Subtract 8 from both sides

• Add 4x to both sides

• Add 8 to both sides

• Subtract 4x from both sides

What is the solution for x in the equation 3x - 4x = -36 + 18?

• x = -8

• x = 18

• x = -18

• x = 8

What form does an equation with no solution take?

• A + B = C

• A = B

• A - B = C

• A = A

Why does the equation x + 7 = x + 4 have no solution?

• The constants are different

• The variables cancel out

• Both sides are equal

• The equation is not linear

What happens when you subtract x from both sides of the equation x + 7 = x + 4?

• You get 0 = -3

• You get 0 = 3

• You get 3 = 0

• You get 7 = 4

What form does an equation with infinite solutions take?

• A = B

• A = A

• A + B = C

• A - B = C

Why does the equation x + 7 = x + 7 have infinite solutions?

• The variables cancel out

• The equation is not linear

• Both sides are equal

• The constants are different