Question

1.

Name the algebraic property demonstrated in the example below: (1 point)
If x = 3 and 3 = y, then x = y.


Commutative Property of Addition

Associative Property of Addition

Transitive Property

Symmetric Property

2.
Name the algebraic property demonstrated in the example below:
3 ⋅ (x ⋅ y) = (3 ⋅ x) ⋅ y


Distributive Property

Transitive Property

Associative Property of Multiplication

Commutative Property of Multiplication

3.
Which of the following describes the correct process for solving the equation 2x − 6 = 22 and arrives at the correct solution?


Divide both sides by −6 and then add 2. The solution is x = 8.

Subtract 6 from both sides of the equation and then divide by 2. The solution is x = 7.

Add 6 to both sides of the equation and then divide by 2. The solution is x = 14.

Add 6 to both sides of the equation and then divide by 22. The solution is x = −14.

4.

Solve 5c + 4 = −26.

6

−6

−4.4

3

5.
Solve 3x − x + 2 = 12.

−5

4

7

5

6.
Solve 3(x + 1) + 6 = 33.


10

8

8.7

−8

7.
Solve y over negative 2 + 5 = 13.


−16

16

−36

36

8.
Solve for x: the quantity of x plus 4 all over 2 = 7.


x = 3

x = 5

x = 6

x = 10

9.
Solve for x: 1 over 4 (2x − 14) = 4.


15

15 over 2

9

11

10.
A water park charges $5 for entry into the park and an additional $2 for each of the big water slides. Steven spent $17 on his visit to the water park. Which equation can be used to find the number of big water slides, x, that Steven went on?

5 + 2x = 17

5x + 2 = 17

5x + 2x = 17

5 + 2 = 17x

Answer 1

Answer with explanation:

1.

It is given that ,

x=3 and 3=y ,then x=y.

This is called Transitive Property ,which states that if a , b and c are three elements in a set , then if , a=b ,b=c ⇒a=c

Option C:→ Transitive Property

2.

It is given that

⇒3 ⋅ (x ⋅ y) = (3 ⋅ x) ⋅ y

For any three real numbers , a,b and c, → a × (b×c)=(a×b)×c

Option C→ Associative Property of Multiplication

3.

The given equation is

2 x -6 =22

To solve the equation

→Add 6 to both sides of the equation

2 x=28

→Dividing by 2 on both sides

x=14

Option C:→ Add 6 to both sides of the equation and then divide by 2. The solution is x = 14.

4.

5 c +4= -26

Subtract -4 from both sides

5 c = -30

Dividing by 5 on both sides

c= -6

Option B

5.

3 x -x +2=12

Subtract 2 from both sides

2 x =12 -2

2 x=10

Dividing by 2 on both sides

x=5

Option D

6.

3 (x+1)+6=33

Subtract 6 from both sides

3 (x+1)= 27

Dividing by 3 on both sides

x+1=9

Subtract 1 from both sides

x=9-1

x=8

Option B

7.

`(y)/(-2)+5=13\\\\ \text{Subtract 5 from both sides}\\\\ (y)/(-2)=8\\\\y= -8 * 2\\\\y= -16`

Option A: y= -16

8.

`\rightarrow (x+4)/(2)=7\\\\\rightarrow \text{Multiplying by 2 on both sides}\\\\\rightarrow x+4=14\\\\\rightarrow x=14-4\\\\\rightarrow x=10`

Option D : x=10

9.

`\rightarrow (1)/(4)* (2 x-14)=4\\\\\text{Multiplying by 4 on both sides}\\\\\rightarrow 2 x-14=16\\\\\text{Adding 14 on both sides}\\\\2 x=30\\\\\text{Dividing both sides by 2}\\\\ \rightarrow x=15`

Option A: 15

10.

Amount charged for entering into water park= $5

Amount charged for additional big water slides = $ 2

Total amount spent by Steven for visit in water park =$ 17

x = the number of slides.

Writing the statement in terms of equation

5 +2 x=17

Option A

Answer 2

1)Transitive Property:

This property suggests that if we have three numbers say a,b and c, such that, a=b and b=c then a=c.

Here x=3 and 3=y. Thus x=y by transitive property.

2) Associative Property of Multiplication:

This property suggests that if we have three numbers, say, a,b and c, then the multiplication of these three numbers with each other will yield the same result, irrespective of their order of multiplication.

Thus, a.(b.c)=(a.b).c

For example: 2.(3.4) = (2.3).4

So, here we have, 3.(x.y) = (3.x).y

3) 2x-6=22

⇒2x-6+6=22+6

⇒2x=28

⇒x=28÷2

⇒x=14

Hence, First add 6 both the sides of the equation and then divide by 2. The answer is 14.

4)
`5c + 4 = −26`

⇒
`5c=-26-4`

⇒
`5c=-30`

⇒
`c=(-30)/(5)`

⇒c=-6

5) 3x-x+2=12

⇒2x+2=12

⇒2x=12-2

⇒2x=10

⇒x=10÷2

⇒x=5

6) 3(x + 1) + 6 = 33

⇒3x+3+6=33

⇒3x+9=33

⇒3x=33-9

⇒3x=24

⇒x=24÷3

⇒x=8

7) y over negative 2 +5=13

`(y)/(-2)+5=13`

⇒
`(y)/(-2)=13-5`

⇒
`(y)/(-2)=8`

⇒y =8 ×(-2)

⇒y = -16

8)

`(x+4)/(2) =7`

⇒
`x+4=14`

⇒
`x=14-4`

x=10.

9) 1 over 4 (2x − 14) = 4

⇒
`(1)/(4)(2x-14)=4`

⇒
`2x-14=16`

⇒
`2x=14+16`

⇒
`2x=30`

⇒
`x=(30)/(2)`

⇒
`x=15`

10) Fixed amount paid as entry fee by Stephen = $5

Let the number of big water slides taken by Stephen be x.

Charge for each big water slide = $2

Thus, charge for 'x' big water slides = $2 × x = $ 2x

So, total amount paid by Stephen = 5 + 2x

Given, Stephen pays $ 17

Thus, 5+2x=17.

This equation can be used to find out the number of big water slides taken by Stephen.