Solving Equations: Key Concepts and Techniques

Why is it important to keep equations balanced when solving them?

• To make the solution easier to find

• To avoid using negative numbers

• To simplify the equation

• To ensure the equation remains true

What is the first step in solving the equation -6n + 4 = -38?

• Add 4 to both sides

• Divide both sides by -6

• Subtract 4 from both sides

• Multiply both sides by -6

Which property of equality is used when subtracting the same number from both sides of an equation?

• Addition property of equality

• Multiplication property of equality

• Subtraction property of equality

• Division property of equality

When simplifying the equation 5a - 3a - 8 + 1 = -19, what is the result of combining like terms?

• 8a - 7 = -19

• 5a - 7 = -19

• 2a - 7 = -19

• 2a + 7 = -19

What is the next step after combining like terms in the equation 5a - 3a - 8 + 1 = -19?

• Add 7 to both sides

• Subtract 7 from both sides

• Divide both sides by 2

• Multiply both sides by 2

In the equation -4p - 2p + 5 = 3p - 8p + 6, what is the result of combining like terms?

• -6p + 5 = 5p + 6

• -6p + 5 = -5p + 6

• -6p + 5 = -5p - 6

• -6p - 5 = -5p + 6

What should you do if you have variables on both sides of an equation?

• Move all constants to one side

• Move all variables to one side

• Add the variables together

• Divide both sides by the variable

How do you know if an equation has no solution?

• The variables cancel out and the remaining statement is false

• The equation has a constant on both sides

• The variables cancel out and the remaining statement is true

• The equation has a variable on both sides

What does it mean if the variables cancel out and the remaining statement is true?

• The equation has infinite solutions

• The equation has all real numbers as solutions

• The equation has one solution

• The equation has no solution

What is the solution set for the equation -3 + 6x = 6x - 3?

• No solution

• x = 3

• All real numbers

• x = 0