Math Problems?

Question

Can any one help me with this.. can you answer all of them..



4x + 3 = - 5

-x + 7 = 12

2t - 8t + 1 = 43

0 = -7n + 4 - 5n

If you can please work them out.

Answer 1

The first thing you do to solve this kind of equations with single variable is to write all the terms with variables(letters) on one side of the equation and the numbers with no variables (no letters) on the other side of the equation.

I will take your first equation as an example:
4x = -5 -3 <-- Notice, the sign of 3 changed when moved to the other side of the equation. This you do whenever you move any term to the other side. Also notice, there are no letters on the right hand-side

Next, we divide both sides by 4, because that’s the number multiplying the variable:

x = -8/4

Therefore:
x= -2 <--- Ans

So, that’s the same idea for all the others. I will not explain the rest ones in detail, so if you have any questions, ask your teacher or classmate.


The second equation:
-x + 7 = 12

Sol.

-x = 12 -7
-x = 5 (divide both sides by -1)
x = -5 <- Ans.

Next,

2t - 8t + 1 = 43
2t - 8t = 43 -1
-6t = 42 (notice that when diff. numbers have the same variable raised at the same power, you can simply add them or subtract them)
t= -7 (both sides were divided by -6)

t= -7 <--- Ans

Last,
0 = -7n + 4 - 5n
7n + 5n = 4
12n = 4 (divide both sides by 12)
n= 4/12 (simply)

n= 1/3 <--- Ans

Hope this actually helps you understand how to do these kinds of problems. :)

Answer 2

4x +3 = -5
use additive inverse to get all knowns on right side of the equation: Additive inverse is change signs and add.

comment these to memory:
a positive plus a positive is a positive
a negative plus a negative is a negative
a negative plus a positive you find the difference and use signal of largest number.

4x + 3 -3 = -5 -3
4x = -8
now divide both sides by 4

4x / 4 = -8 / 4

also comment these to memory:
a negative divided by a positive is a negative
a positive divided by a negative is a negative..
a negatvie divided by a negative is a positive
a positive divided by a positive is a positive. .

x = -2 is your answer. now you check you answer by plugging it in the formula.

4*(-2) +3 = -5
-8 +3 = -5
-5 - -5

- x + 7 = 12
take additive inverse and add it to both sides of the equation>

- x +7 - 7 = 12 - 7

- x = 5 but we are not done yet. Notice the - x. You do not want to leave the varible a negative unless you cannot get out of it.

to clear the negative from our varible we divide both sides by a - 1

- x / -1 = 5 / -1

x = - 5
on check your work:

- (-5) +7 = 12 Note the double negative: what is happening is that there is an understood 1 which actually makes it
1*x anytime you x the 1 is understood

what we have is:
- 1*x + 7 =12
- 1* (- 5) + 7 = 12
negative times a negative is a positive: so - 1 * -5 = + 5

5 + 7 =12
12 =12

2t - 8t +1 = 43
combine like terms in this case 2t and 8t using rules of signed numbers: I gave you above:

- 6t + 1 = 43
now using additive inverse to move 1 to right side of equation sign:

- 6t + 1 - 1 = 43 -1
- 6t = 42
divide both sides by - 6

t = - 7
now check your work always and show it on paper.

2* (-6) - 8* (- 6) + 1 = 43

- 12 +48 +1 = 43
37 = 43 Oops got something wrong: see how easy it is that is why you check your work always.

2* (- 7) - 8 * (-7) + 1 = 43

- 14 + 56 +1 =43
43 = 43

0 = - 7n +4 - 5n what I always do is get all my literal numbers on the left side of the equation by rewriting the equation but that is up to you some people like working left some right:

- 7n + 4 - 5n =0
now use associative rule to get like terms together.

- 7n - 5n + 4 = 0
now additive inverse to move the 4 to the left side of the equation sign.

- 7n - 5n +4 - 4 = 0 - 4
-7n -5n = -4
now add like terms. - 7n - 5n is going to give you -12 n rules of addition with signed numbers.

- 12n = -4
now divide both sides by - 12

- 12n / -12 = - 4 / -12
left side first:

n = - 4 / - 12 a fraction so reduce by using a -4 since it will go into both top and bottom of the fraction:

n = 1 / 3
you see why I used a - 4 to reduce? It was to clear the - signs out.
Now we check it:

- 7 (1/3) +4 - 5(1/3) =0

- 7 /3 +4 - 5 /3 = 0

Oops pesty fractions common denomiator time:

4 is how many thirds: 12 thirds isn't it?

- 7/3 + 12/3 -5/3 =0
0/3 is 0 don't forget that.
0/3 = 0
0 =0
Hope that helped comment to memory what I told you to comment to memory.
n=

Answer 3

1) x= -2
2) x= 5
3) t= -7
4) n= 3/4

Answer 4

1. -2
2. 5
3. -7
4. 3/4