Can you answer these 2 simple questions about alegbra, please?

Question

When dividng on both sides of the equation, the x sign remains, right?

Example 2x=10, divide both sides by 2 to isolate x. In fact 2x divided by 2 is equal to 1x, or just x.

My confusion is with when handling division.

Example 10/x=5. You multiply both sides by x and it becomes 10=5x. Why is it that when multiplying 10/x by x, it removes the x?

Also, how do I solve this?

100/(2x+1) = 20

Answer 1

100/(2x + 1) = 20

Multiply both sides by (2x + 1)

100 = 20(2x + 1)

Expand the right hand side.

100 = 40x + 20

Isolate x.

80 = 40x
80/40 = x
2 = x

Answer 2

100/(2x+1)=20
multiply by (2x+1)
100=20(2x+1)
100=40x+20
40x=100-20
x=80/40
x=2

To answer you question when you multiply 10/x by x, it doesn't actually remove it. It becomes 10/x*x (10 divided by x and then multiplied by x). But anything multiplied and then divided by the the same number remains the same in the end. For example: 20/5*5 becomes 4*5 and then 20. That's called canceling out. It might help you to write these things out, therefore when you divide or multiple both sides of an equation by something, don't take the shortcut but write it out completely.
Thus, as in the example above, when I multiplied 100/(2x+1)=20 by (2x+1), I skipped one step. You can write 100/(2x+1)*(2x+1)=20*(2x+1). This should help you see the why both (2x+1) should be removed from the left side.

Answer 3

1x and x are the exact samething. Since any number multiply by 1 is equal to itself. 1 * x = x

10/x = 5

when you multiply x for both sides, x cancel out because when a number divide by itself will equal to 1

x(10) / x = 5x, which is the same as:
x/x * 10 = 5x
1 * 10 = 5x
10=5x

100/(2x+1) = 20

multiply (2x +1) for both sides
100 = 20(2x+1)

distribute
100 = 40x + 20

subtract 20 for both sides
40x = 80

divide 40
x = 2

Answer 4

"x" is a variable, not a sign.

In 10/x = 5 x does not disappear, it moves to another part of the equation. You should make sure you do not include cases in which a denominator is zero when presenting your solution.

100/(2x + 1) = 20 // multiply by 2x + 1

100 = 20(2x + 1)

100 = 40x + 20 // subtracting 20

80 = 40x //dividing by 40

x=2

Let's check our solution
2x+1 = 2*2+1 = 5
It is not zero so we can divide 100 by it

100/(2x + 1) = 100/5 = 20

Answer 5

10/x times x/1.... cross multiplying cancels out the X.

multiply both sides by (2x+1).

then, you have 100 = 20 (2x+1)
5 = 2x + 1
4 = 2x
2 = x

Answer 6

firstly it is just like subtraction and addition, if you subtract 10x when the equation is adding 10x the x's are cancelled out.

for the equation, you must use the distributive property. it is

100/(2x+1)=20

then multiply it by (2x+1)

now its... 100=20 (2x+1)

then distribute... 100=20(1) +20 (2x)

then simplify... 100=20+40x

then subtract 20... 80=40x

then divide by 40= 2=x

the answer is 2