Math  /  Algebra

QuestionSimplify each expression.
1. 9y+4.16y9 y+4.1-6 y
2. 3x+5+7x-3 x+5+7 x
3. 8x+133x+9128 x+13-3 x+9 \frac{1}{2}
4. y2+3y2y^{2}+3 y^{2}
5. 4x+153x+104 x+15-3 x+10
6. 10x+2x+8x-10 x+2 x+8 x

Studdy Solution

STEP 1

1. Each expression involves combining like terms.
2. Like terms are terms that have the same variable raised to the same power.
3. Constants are combined separately from variable terms.

STEP 2

1. Identify and combine like terms for each expression.
2. Simplify the resulting expression.

STEP 3

For expression 1: 9y+4.16y9y + 4.1 - 6y
Identify like terms: 9y9y and 6y-6y.
Combine like terms:
9y6y=3y 9y - 6y = 3y
The simplified expression is:
3y+4.1 3y + 4.1

STEP 4

For expression 2: 3x+5+7x-3x + 5 + 7x
Identify like terms: 3x-3x and 7x7x.
Combine like terms:
3x+7x=4x -3x + 7x = 4x
The simplified expression is:
4x+5 4x + 5

STEP 5

For expression 3: 8x+133x+9128x + 13 - 3x + 9 \frac{1}{2}
Identify like terms: 8x8x and 3x-3x.
Combine like terms:
8x3x=5x 8x - 3x = 5x
Combine constants:
13+912=22.5 13 + 9 \frac{1}{2} = 22.5
The simplified expression is:
5x+22.5 5x + 22.5

STEP 6

For expression 4: y2+3y2y^2 + 3y^2
Identify like terms: y2y^2 and 3y23y^2.
Combine like terms:
y2+3y2=4y2 y^2 + 3y^2 = 4y^2
The simplified expression is:
4y2 4y^2

STEP 7

For expression 5: 4x+153x+104x + 15 - 3x + 10
Identify like terms: 4x4x and 3x-3x.
Combine like terms:
4x3x=1x 4x - 3x = 1x
Combine constants:
15+10=25 15 + 10 = 25
The simplified expression is:
x+25 x + 25

STEP 8

For expression 6: 10x+2x+8x-10x + 2x + 8x
Identify like terms: 10x-10x, 2x2x, and 8x8x.
Combine like terms:
10x+2x+8x=0x -10x + 2x + 8x = 0x
The simplified expression is:
0 0

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