Multiple Solution Techniques for Linear Equations and Inequalities

What is the main idea discussed in the introduction regarding solving equations?

• There is only one correct way to solve equations.

• Different methods can lead to the same solution.

• Only inequalities can be solved in multiple ways.

• Equations cannot be solved using the distributive property.

How does the distributive property simplify the expression 4(x - 9)?

• 4x + 36

• 4x - 36

• 4x + 9

• 4x - 9

What is the solution to the equation 7x = 5x + 16 after gathering like terms?

• x = 8

• x = 16

• x = 4

• x = 2

When solving the inequality 4x - 9 > 11x + 26, what is the result after moving 4x to the right?

• 9 < 7x + 26

• 9 > 7x + 26

• -9 > 7x + 26

• -9 < 7x + 26

What must be remembered when dividing both sides of an inequality by a negative number?

• The inequality sign remains the same.

• The inequality sign is switched.

• The inequality sign is removed.

• The inequality becomes an equation.

What is the least common multiple of 2 and 3 used for in solving equations with fractions?

• To add fractions

• To subtract fractions

• To multiply fractions

• To find common denominators

What is the solution to the equation x/2 + 1/4 = x/3 after finding common denominators?

• x = -3/2

• x = -1/2

• x = 1/2

• x = 3/2