Solving Linear Equations in One Variable

The video tutorial covers solving linear equations in one variable, starting with an introduction to the process and steps involved. It includes multiple examples demonstrating how to simplify equations and solve for variables using properties of equality. The tutorial also addresses common mistakes and special cases like contradictions and identities. Finally, it provides practice problems for further understanding.

What is the first step in simplifying a linear equation?

• Combine like terms

• Distribute and clear fractions

• Use the addition property of equality

• Use the multiplication property of equality

In the equation 4u - 12u - 16 = -52, what is the result of combining like terms?

• -8u - 16

• 4u - 16

• -8u + 16

• 4u + 16

After simplifying the equation 4u - 12u - 16 = -52, what is the next step?

• Multiply both sides by -8

• Add 16 to both sides

• Subtract 16 from both sides

• Divide both sides by -8

In the equation -3(u - 1) = 8u + 37, what is the result of distributing -3?

• -3u - 3

• -3u + 3

• 3u + 3

• 3u - 3

What is the final simplified form of the equation -3(u - 1) = 8u + 37 before solving for the variable?

• -3u - 3 = 8u + 37

• -3u + 3 = 8u + 37

• -3u - 3 = 8u - 37

• -3u + 3 = 8u - 37

In the example where a student made a mistake, what was the correct step after subtracting 15x from both sides?

• Divide both sides by 4

• Add 8 to both sides

• Set the equation equal to zero

• Multiply both sides by 4

What is the correct interpretation when the variable disappears and the statement is false?

• Infinite solutions

• All real numbers are solutions

• No solution

• One solution

What is the correct interpretation when the variable disappears and the statement is true?

• All real numbers are solutions

• No solution

• One solution

• Infinite solutions

In the equation 6x - 12 + 2x = 4(2x - 3), what is the result of combining like terms on the left side?

• 6x + 12

• 8x + 12

• 6x - 12

• 8x - 12

What is the final simplified form of the equation 6x - 12 + 2x = 4(2x - 3) before solving for the variable?

• 8x - 12 = 8x - 12

• 8x - 12 = 8x + 12

• 6x - 12 = 8x - 12

• 6x - 12 = 8x + 12