MA.8.1.2 MA.8.1.3

Linear Expressions 8th Grade

Florida - Benchmarks for Excellent Student Thinking: MA.8.1.2
Apply properties of operations to multiply two linear expressions with rational coefficients.
Florida - Benchmarks for Excellent Student Thinking: MA.8.1.3
Rewrite the sum of two algebraic expressions having a common monomial factor as a common factor multiplied by the sum of two algebraic expressions.

To solve an equation for an unknown value,
keep the equation balanced while isolating the unknown.

Example:

First, divide both sides of the equation by 6.
Then, subtract 4.2 from both sides of the equation.

Example:

First, simplify the equation.

6(x + 3)	=	3(x + 10)
6x + 18	=	3x + 30

Next, use opposite operations to solve for x.

For a linear equation, there are three types of solutions:
no solution, one solution, and infinitely many solutions.

If a linear equation can be transformed to the form a = b, where a and b are different numbers, then the equation has no solution.
If a linear equation can be transformed to the form x = a, where x is a variable and a is some number, then the equation has exactly one solution.
If a linear equation can be transformed to the form a = a, where a is some number, then the equation has infinitely many solutions.

Example:

Simplify the equation until it is in the form x = a, a = a, or a = b.

The equation simplifies to 22 = 22, which is in the form a = a.
So, the equation has infinitely many solutions.

Sometimes in math, it is necessary to
translate words into mathematical expressions.

Here are some keys to translating words into mathematical expressions.

RECOGNIZE WHICH OPERATIONS TO USE.
Below is a list of commonly seen words and the correlating operation.

ADDITION	more than, increase, plus, sum
SUBTRACTION	less than, decrease, minus, difference
MULTIPLICATION	times, product
DIVISION	quotient

ENSURE CORRECT ORDER OF OPERATIONS.
The order of operations is listed below.

REPRESENT VALUES.
When a value is unknown, it is typically represented by a variable or symbol.

Example:

Translate the descriptions of operations.
Use a variable to represent "some number."

decrease 13 by	→	13 −
product of 4 and some number	→	4x
decrease 13 by the product of 4 and some number	→	13 − 4x

Example:

Translate the descriptions of operations.
Use a variable to represent "some number."

sum of 12 and some number	→	12 + x
6 times the sum of 12 and some number	→	6(12 + x)

Linear Expressions