name
class
date
good luck! show all your work and circle the final answer.
1. which property of addition is shown? ( a + b = b + a )
2. evaluate the expression.( 3(2x + 1)+4x;x = 4 )
3. there are 39 chocolates in your treat bag and additionally you receive 4 chocolates per house after trick or treat. how many chocolates are in your treat bag after visiting 11 houses?
4. simplify expression. ( 4m + 5+5m + 2 )
5. simplify expression. ( 3x + 4y-8x - 3y )
6. solve.( 2y - 7 = 8 - 3y )
7. solve ( 7x - 8 = 5x + 10 )
8. solve ( -5x + 2x-7 + 1 = 6 )
9. let x be the first number. write the two consecutive numbers
10. the sum of three consecutive integers is 48. find those integers.
11. solve ( 2(3x - 5)=2x + 2 )

Question

Accepted Answer

# 1.
## Brief Explanations:
The property $a + b=b + a$ is the commutative property of addition.
# Answer:
Commutative property of addition

# 2.
## Step1: Substitute $x = 4$ into the expression
Substitute $x = 4$ into $3(2x + 1)+4x$. First, calculate $2x+1$ when $x = 4$: $2\times4+1=8 + 1=9$. Then $3(2x + 1)=3\times9 = 27$, and $4x=4\times4 = 16$
## Step2: Add the results
$3(2x + 1)+4x=27+16$
# Answer:
$43$

# 3.
## Step1: Set up an equation
Let the number of chocolates received per house be $x$. The initial number of chocolates is $39$. After visiting $n = 11$ houses, the total number of chocolates $y=39+11x$. Assuming $x = 4$ (since it's not specified otherwise, but if we assume a value from the problem - like maybe similar to problem 2's $4x$ context, if we take $x = 4$)
## Step2: Calculate the total
$y=39+11\times4=39 + 44$
# Answer:
$83$

# 4.
## Step1: Combine like - terms
For $4m+5 + 5m+2$, combine the $m$ terms: $4m+5m=(4 + 5)m=9m$, and combine the constant terms: $5+2=7$
# Answer:
$9m + 7$

# 5.
## Step1: Combine like - terms
For $3x+4y-8x - 3y$, combine the $x$ terms: $3x-8x=(3 - 8)x=-5x$, and combine the $y$ terms: $4y-3y=(4 - 3)y=y$
# Answer:
$-5x + y$

# 6.
## Step1: Add $3y$ to both sides
$2y-7+3y=8-3y + 3y$, which simplifies to $5y-7=8$
## Step2: Add $7$ to both sides
$5y-7 + 7=8+7$, so $5y=15$
## Step3: Divide both sides by $5$
$y=\frac{15}{5}$
# Answer:
$y = 3$

# 7.
## Step1: Subtract $5x$ from both sides
$7x-8-5x=5x + 10-5x$, which gives $2x-8=10$
## Step2: Add $8$ to both sides
$2x-8 + 8=10+8$, so $2x=18$
## Step3: Divide both sides by $2$
$x=\frac{18}{2}$
# Answer:
$x = 9$

# 8.
## Step1: Combine like - terms
$-5x+2x-7 + 1=6$ simplifies to $-3x-6=6$
## Step2: Add $6$ to both sides
$-3x-6+6=6+6$, so $-3x=12$
## Step3: Divide both sides by $-3$
$x=\frac{12}{-3}$
# Answer:
$x=-4$

# 9.
## Brief Explanations:
If $x$ is the first number, the next consecutive number is $x + 1$
# Answer:
$x,x + 1$

# 10.
## Step1: Set up an equation
Let the first integer be $x$, the second be $x + 1$, and the third be $x + 2$. Then $x+(x + 1)+(x + 2)=48$
## Step2: Simplify the left - hand side
$x+x + 1+x + 2=3x+3$
## Step3: Solve for $x$
$3x+3=48$, subtract $3$ from both sides: $3x=48 - 3=45$, then $x=\frac{45}{3}=15$
## Step4: Find the other integers
The second integer is $x + 1=16$, the third integer is $x + 2=17$
# Answer:
$15,16,17$

# 11.
## Step1: Expand the left - hand side
$2(3x-5)=6x-10$, so the equation becomes $6x-10=2x + 2$
## Step2: Subtract $2x$ from both sides
$6x-10-2x=2x + 2-2x$, which gives $4x-10=2$
## Step3: Add $10$ to both sides
$4x-10+10=2+10$, so $4x=12$
## Step4: Divide both sides by $4$
$x=\frac{12}{4}$
# Answer:
$x = 3$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1.

Answer:

2.

Step1: Substitute \(x = 4\) into the expression

Step2: Add the results