In the following activity, write an equation to represent each verbal statement, and use it to find the value of each unknown number. Then, put the solution values in order from smallest to largest. [Note: The smallest solution is "first", and the largest solution is "fifth".]


1. fourth


Half of a number is added to four. This sum is equivalent to negative one.


2. first


The sum of a number and three is divided by five. The result is negative two.


3. third


The difference between four times a number and five has a result of negative eight.


4. second


The difference between a number and five is multiplied by negative two. The

resulting product equals fourteen.


5. fifth


The sum of a number and two is equal to the quotient of six and negative four.




I WILL GIVE BRAINLEST

Answer:

First x=-13 (The sum of a number and three is divided by five. The result is negative two.)

Second x=-10 (Half of a number is added to four. This sum is equivalent to negative one.)

Third x=-3.5 (The sum of a number and two is equal to the quotient of six and negative four.)

Fourth x=3.25 (The difference between four times a number and five has a result of negative eight.)

Fifth  x=12 ( The difference between a number and five is multiplied by negative two. The  resulting product equals fourteen. )

Step-by-step explanation:

We will consider number = x

1. Half of a number is added to four. This sum is equivalent to negative one.

[tex]\frac{1}{2}x+4=-1[/tex]

Now solving to find value of x

[tex]\frac{1}{2}x+4=-1\\\frac{1}{2}x=-1-4\\\frac{1}{2}x=-5\\x=-5*2\\x=-10[/tex]

So, value of x=-10

2. The sum of a number and three is divided by five. The result is negative two.

[tex]\frac{x+3}{5}=-2[/tex]

Solving:

[tex]\frac{x+3}{5}=-2\\x+3=-2*5\\x+3=-10\\x=-10-3\\x=-13[/tex]

So, value of x=-13

3. The difference between four times a number and five has a result of negative eight.

[tex]4x-5=-8[/tex]

Solving:

[tex]4x-5=8\\4x=8+5\\4x=13\\x=13/4\\x=3.25[/tex]

So, value of x=3.25

4. The difference between a number and five is multiplied by negative two. The  resulting product equals fourteen.

[tex](x-5)*-2=-14[/tex]

Solving

[tex](x-5)*-2=-14\\-2x+10=-14\\-2x=-14-10\\-2x=-24\\x=-24/-2\\x=12[/tex]

So, value of x=12

5. The sum of a number and two is equal to the quotient of six and negative four.

[tex]x+2=\frac{6}{-4}[/tex]

Solving:

[tex]x+2=\frac{6}{-4}\\x+2=-\frac{3}{2}\\x= -\frac{3}{2}-2\\x=\frac{-3-2*2}{2} \\x=\frac{-3-4}{2} \\x=\frac{-7}{2} \\x=-3.5[/tex]

So, value of x=-3.5

Now arranging based on values of x

x=-10, x=-13, x=3.25, x=12, x=-3.5

First x=-13 (The sum of a number and three is divided by five. The result is negative two.)

Second x=-10 (Half of a number is added to four. This sum is equivalent to negative one.)

Third x=-3.5 (The sum of a number and two is equal to the quotient of six and negative four.)

Fourth x=3.25 (The difference between four times a number and five has a result of negative eight.)

Fifth  x=12 ( The difference between a number and five is multiplied by negative two. The  resulting product equals fourteen. )

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