Expressions & Equations

Simplifying Expressions & Writing Equations

Simplifying Expressions

• When we simplify an expression, we remove any parentheses and combine all like terms

• We can use properties such as the Commutative and Distributive Properties

• Remember, like terms are terms that have the same variable or are constants.

• For example, 3x and 5x are like terms because they both have 'x'.

• Also, 8 and -10 are like terms because they are both constants.

Multiple Select

Which of the following is a like term for 6y? Check all that apply.

• 6

• y

• 2y

• -15.5y

Simplifying Expressions

• When we write an expression in simplified form, it is called STANDARD form

• The opposite of standard form is expanded form

• 8a + 3a is an expression in expanded form.

• 11a is that same expression in standard form.

Multiple Choice

Which option below is an equivalent expression for 8b + 8 - 3b written in standard form?

• 11b + 8

• 8 - 3b + 8b

• -5b + 8

• 5b + 8

Simplifying Expressions Using the Distributive Property

• "Distributing" a number means you are multiplying EACH term on the inside of the parentheses by the number on the outside.

• Be careful of your signs!

Multiple Choice

Write the following expression in standard form.

9m - 3(-2m + 3)

• 15m - 9

• 6m - 9

• -6m + 9

• 3m - 9

Multiple Choice

Write the following expression in standard form.

4y - (3 + y)

• 4y - 3 - y

• 5y - 3

• 3y - 3

• 5y + 3

Factored Form

• Find a common factor between the terms

• Divide each term by that factor

• The common factor goes on the outside of the parentheses and the quotients go on the inside.

Multiple Choice

Write the following expression in factored form.

8j + 10 - 12k

• 2(4j + 5 - 12k)

• 2(4j + 5 - 6k)

• 4(2j + 5 - 6k)

• 2(4j - 5 - 6k)

Equations

• Equations are statements of equality

• The left side must = the right side

• To check if a number is a solution to the equation, substitute it in the equation and check to see if the left = right.

Multiple Choice

Is x = 10 a solution for the following equation?

-4x + 10 = -20 - x

• Yes

• No

Multiple Choice

Is z = -4 a solution to the equation below?

6z - 5 = -19

• Yes; the left side equals -19

• No; the left side equals -29

• No; the left side equals -24

• No, the left side equals 19

Multiple Choice

Which of the following is an equation representing the sum of two consecutive integers is 91? (The smallest integer is represented by n)

• n + 1 = 91

• n + (n + 1) = 91

• n + 2 = 91

• n + (n + 2) = 91