Solving Linear Equations and Expressions

The video tutorial covers various mathematical concepts for eighth-grade students, including constant terms in expressions, analyzing equations for solutions, determining the truth of equations, solving equations step-by-step, analyzing points on a graph, and understanding triangle rotation. Each section provides detailed explanations and examples to help students grasp these concepts effectively.

What is a constant term in an expression?

• A term that is always zero

• A term that remains unchanged regardless of the variable

• A term that changes with the variable

• A term that includes a variable

In the expression 8 - 4y, what is the constant term?

• 8

• -4

• y

• 4y

Why does Lynn believe there are no solutions to her equation?

• Because the left side and right side are not equal

• Because the equation has a constant term

• Because the left side has more variables

• Because the equation is balanced

What mistake did Han make in his reasoning about the equation?

• He solved the equation correctly

• He forgot to include a variable

• He assumed the equation had no solutions

• He added the constants incorrectly

Which equation is true for all values of x?

• -2x + 4 = -3x + 4

• 6x - 4 = -4 + 6x

• 4x - 6 = 4x + 3

• x + 2 = x + 2

How many solutions does the equation 4x - 6 = 4x + 3 have?

• Infinite solutions

• No solutions

• One solution

• Two solutions

What is the solution to the equation 3x = 21?

• x = 0

• x = 3

• x = 21

• x = 7

What is the value of x in the equation 2x = 4/3?

• x = 3/2

• x = 2/3

• x = 1/3

• x = 4/3

Are the points (2, 6) on the same line as (-2, 0) and (0, -6)?

• No, (2, 6) does not lie on the line

• Yes, they all lie on the same line

• No, because the line is vertical

• Yes, but only if the line is extended

What is the measure of angle D' if angle D is 45 degrees?

• 45 degrees

• 30 degrees

• 90 degrees

• 60 degrees