Solving Equation by Properties of Equality

If a = b, what can you add to both sides?

• You can only add zero to both sides.

• Any value (e.g., c) can be added to both sides.

How do you solve for x in the equation x + 5 = 12?

• 6

• 7

• 8

• 10

What does the subtraction property of equality state?

• If a = b, then a * c = b * c for any c.

• If a = b, then a - c = b - c for any c.

• If a = b, then a + c = b + c for any c.

If 3x = 12, what is the value of x?

• 2

• 8

• 6

• 4

What is the multiplication property of equality?

• If a = b, then a - c = b - c for any non-zero c.

• If a = b, then a / c = b / c for any non-zero c.

• If a = b, then a + c = b + c for any non-zero c.

• If a = b, then a * c = b * c for any non-zero c.

How do you isolate a variable in an equation?

• Use inverse operations to move other terms away from the variable.

• Add the variable to both sides of the equation.

p+5 =10

• p = 5

• p = 10

• p = 15

• p = -5

What is the division property of equality?

• If a = b, then a * c = b * c for any non-zero c.

• If a = b, then a - c = b - c for any c.

• If a = b, then a/c = b/c for any non-zero c.

• If a = b, then a + c = b + c for any c.

How can you check if your solution to an equation is correct?

• Graph the equation and check the intersection point.

• Use a calculator to find the solution.

• Ask a friend if your answer is correct.

• Substitute the solution back into the original equation and verify equality.

What property of equality is used to solve the equation x+4=12 by subtracting 4 from both sides?

• Division property

• multiplication property

• Subtraction property

• Addition property