5x-x=-12, -9-b-8b=-23, 4(y-1)=36, 21=2(4a+2),...

[denimcottoncandy]

I do not know how to do these problems. Please help me, don't just give me the answers! I am really stuck, and I am aslo in tears.

1) 5x-x=-12

2) -9-b-8b=-23

3) 4(y-1)=36

4) 21=2(4a+2)

5) 1/3(x-12)=8

Please help me out here.
Thankyou

 

[tkhunny]

Is there a problem statement? What is to be done?

What do you know about:

"Like Terms"
"Distributive Property of Multiplication over Addition"

 

[Denis]

Your math teacher has asked you to solve those, but has not taught how?
Or were you absent from math class?

 

[stapel]

I do not know how to do these problems.

It is unfortunate that this topic was not covered in class or in your book. (The tutors can help students work through specific exercises, but only if the student has a basic understanding of the underlying material.) Since we cannot provide the missing classroom instruction, please use online resources instead.

Once you have studied a few lessons on how to solve linear equations, so you have a basic grasp of the terms and techniques, please attempt the exercises. If you get stuck, please reply showing how far you have gotten.

Thank you.

Eliz.

 

[Trebor]

Firstly, you need to know how to manipulate equations. There are 4 operations: addition, subtraction, multiplication and division.

Addition:

a - 7 = 3

In this example, you can add 7 to both sides of the equation:

a - 7 + 7 = 3 + 7
a = 10 (Check: 10 - 7 = 3)

Subtraction:

b + 5 = -2

Again, you can subtract 5 from both sides of the equation:

b + 5 - 5 = -2 - 5
b = -7 (Check: -7 + 5 = -2)

Multiplication:

Sometimes you will get fractions in an equation, like in this example:

c / 2 = 5

Multiply both sides by 2:

c / 2 * 2 = 5 * 2
c = 10 (Check: 10 / 2 = 5)

Division:

You can also divide both sides of an equation:

4d = 20

Divide both sides by 4

4d / 4 = 20 / 4
d = 5 (Check 4 * 5 = 20)

Please note that with all of these, you can also use variables in the operations, like in this example:

12 / x = 3

Multiply by x:

12 / x * x = 3 * x
12 = 3x
3x = 12
3x / 3 = 12 / 3
x = 4

Some other techniques which you will need:

Like terms:

The first two question involve collecting like terms. Here is a few examples:

6x + 3x = 9x since 6 + 3 = 9
10y - 3y = 7y since 10 - 3 = 7

This only works if the terms are described as 'like' - they have to have the same variable (x, y, z, k, a, b, c, etc.). Here is another example:

6a + 9b - 3a + 10b - c = 3a + 19b - c

Here you cannot simplify more than the right-hand expression, since none of the terms are like.

Expanding brackets:

Whenever you multiply an expression in brackets by another number, use the following method:

a(b + c) = ab + ac

For example:

5 * (9 - 7) = 5 * 9 - 5 * 7 = 45 - 35 = 10

You can check this:

5 * (9 - 7) = 5 * 2 = 10

Your equations:

Now you know everything to solve your equation and similar ones you will see in the future. To help you, I have also included the steps needed to solve them.

1. Collecting like terms.
Division
2. Collecting like terms.
Addition
Division
3. Expanding brackets
Addition
Division
4. Expanding brackets
Subtraction
Division
5. There are several routes to solve this one, but you basically need to multiply by the bottom expression on the fraction.