Linear Equations

Vocabulary

1

number or quantity placed with a variable

coefficient

2

a(b+c) = ab + ac

distributive property

3

an equation where the variable(s) have an exponent of 1

linear equation

4

terms that have the same variable raised to the same power

like terms

5

any numbers that can be expressed in the form a/b, where a and be are integers and b is not equal to 0.

rational number

Combining Like Terms

1

5b²+7b-2b³-12+b³-8b+7

-b³+5b²-b-5

2

3p-(5/6)n+(7/2)(n-(2/3)p)

(8/3)n+(2/3)p

3

5xy+10xz-12xy+4zx+3x²y-2zy

-7xy+14xz-2yz+3x²y

4

(3/5)x-(9/10)y+5(x+2y)

(28/5)x+(91/10)y

5

((3/2)x+(5/8))y+(1/3)x+(6/7)y

(3/2)xy+(1/3)x+(83/56)y

Multi-Step Equations

1

(1/7)x-12= 20

x = 224

2

(4/9)(x+2) = (1/2)(x+5)

x = -29

3

7(5x-3) = 13

x= 34/35

4

8x = (1/12)((3/4)+(1/6)x)

x = 9/1150

5

(3/5)x(2)- (2/7)(x-3) = 6

x = 45/8

Always, Sometimes, or Never

1

Linear equations have one solution

Sometimes

2

If a variable doesn't have a coefficient, it is assumed to be negative one

Never

3

any number under a square root is a rational number

Sometimes

4

When adding or subtracting two fractions, you need to find a common denominator

Always

5

When using the distributive property, if the term on the outside the parenthesis is negative, then the sign of each inside term will change

Always