# Vocabulary - PowerPoint PPT Presentation

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Bell Ringer: Simplify by combining like terms A. 3x +-5x+y B. -2/3x-2-7 C. –x+7y-x D. -7-8+x+y-4x. Vocabulary. Term- Is each piece of an expression. For example: -3x+3y-8-5x there are 4 terms in this expression. -3x, 3y, -8, and -5x

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Vocabulary

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## Bell Ringer: Simplify by combining like termsA. 3x+-5x+yB. -2/3x-2-7C. –x+7y-xD. -7-8+x+y-4x

### Vocabulary

• Term- Is each piece of an expression.

• For example: -3x+3y-8-5x there are 4 terms in this expression. -3x, 3y, -8, and -5x

• Like Term- To simplify an expression, add the coefficients of the similar terms and add the integers.

• For example: -3x, -5x, -3x+-5x=-8x

• Non Example: -3x, 3y or -5x, -8 Neither sets have are like terms because they do not have the same variables.

• Coefficient- Is the number attached to the variable.

• For example: -3x , the coefficient of this term is -3

• Numbers/Intergers are not consider a coefficient. Such as -8

### Caution! Caution!

1. The sign to the left of the term goes with the term

• For example: -3x+2x-9+y

• The terms of this expression are -3x, 2x, -9, y

2. If there is NOT a coefficient attached to a variable then we can assume the coefficient is 1.

• For example: x-y the coefficient of x is 1 and the coefficient of y is -1.

-3x-(-5x)+y

-2/3x-2-7

–x+7y-x

-7-8+x+y-4x

### Caution! Caution!

• Adding: When adding opposite signs subtract the absolute value of the larger number minus the absolute value of the smaller number. Keep the sign of the larger number

• EX. -4+9 =9-4= 5 it is a positive because the positive 9 was larger

• Subtracting: When subtracting a negative sign change both the minus sign and the negative sign to a positive.

• Ex. -9-(-8) = -9+8=-1

### Solving an Equation with fractions

Steps

Remove fractions by multiplying both sides by the multiplicative inverse

Simplify and rewrite

Add or subtract constant and simplify

2/3(x+6)=20

3/2(2/3(x+6)=20(3/2)

X+6=60/2

x+6=30

X+6-6=30-6

X=24

### Equation

Y+2=-9

y+2-2=-9-2

Y=(-9)+(-2)

Y=-11

Y+6=4

y+6-6=4-6

Y=(4)+(-6)

Y=-2

1/2(x+4)=6

2/1(1/2(x+4))=6(2/1)

X+4=12/1

X+4=12

X-4+4=12-4

X=(12)+(-4)

X=8

2/5(z-4)=-10

Z-4=-10(5/2)

Z-4=-50/2

X-4=-25

X-4+4=-25+4

X=-21

2/3(x-6)=5+(-11)

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

X-6=-18/2

X-6=-9

X-6+6=-9+6

X=(-9)+(6)

X=-4

5/7(x-7)=-8+3

X-7=7/5(-5)

X-7=-35/5

X-7=-7

X-7+7=-7+7

X=(-7)+(7)

X=0

3(x-2)-4(x+4)=25

3x-6-4x-16=25

(3x)+(-4x)+(-6)+(-16)=25

-1x-22=25

-1x-22+22=25+22

-1x=47

-1/-1x=47/-1

X=-47

-5(x-7)-8(x-5)=62

-5x+35-8x+40=62

(-5x)+(-8x)+(35)+(40)=62

-13x+75=62

-13x+75-75=62-75

-13x=(62)+(-75)

-13x=-13

-13x/-13=-13/-13

X=1

4(d-2)=3d+(6+d)

4d-8=(3d)+(1d)+(6)

4d-8=4d+6

4d-4d-8=4d-4d+6

-8=6

There is no solution to this problem. -8 can never equal 6.

6x+4=2(3x+2)

6x+4=6x+4

Identity/ All real numbers

6x-6x+4=6x-6x+4

4=4

There are infinite number of solutions. X can equal any real number.

### Class work/ Homework

Complete P.55& 100 Worksheet both front and back. Due Wednesday.

Complete Take Home Test

p.185 2, 4-14,17, 23, 26-29. Due Friday