Solving Linear Equations and Inequalities

The video tutorial covers solving linear equations and inequalities, starting with an introduction and activity. It explains the general form of linear equations, solving equations with multiple factors, and fractional equations. The lesson concludes with a homework assignment.

What is the first step in solving the equation 4x + 8 = 4?

• Divide both sides by 4

• Subtract 8 from both sides

• Multiply both sides by 4

• Add 8 to both sides

Why does the equation 2x - 6 = 1 + 2(x + 3) have no solution?

• The equation is a contradiction

• The equation has infinite solutions

• The equation is undefined

• The equation is inconsistent

What is the solution set for the equation 2x + 10 = 5 + 1(5 + 2x)?

• x = 0

• No solution

• All real numbers

• x = 5

What is the solution for the equation 3x = 0?

• No solution

• x = 3

• x = -3

• x = 0

What is the general form of a linear equation in one variable?

• a/x + b = 0

• ax + by = c

• ax^2 + bx + c = 0

• ax + b = 0

If a = 0 and b ≠ 0 in the equation ax + b = 0, what is the solution set?

• All real numbers

• No solution

• x = -b/a

• x = 0

How do you solve an equation with two linear factors, such as (ax + b)(cx + d) = 0?

• Add the factors

• Divide the factors

• Multiply the factors

• Set each factor to zero

What is the solution set for the equation (x - 1)(x + 2)(x - 3) = 0?

• x = 1, 2, 3

• x = -1, 2, -3

• x = -1, -2, -3

• x = 1, -2, 3

What must be true for a fractional linear equation to be valid?

• Denominator must be greater than zero

• Denominator must not be zero

• Numerator must not be zero

• Both numerator and denominator must be zero

What is the solution for the equation 3x - 7 / (x + 1) = 0?

• x = 0

• x = 7/3

• x = -1

• x = 1