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vodka [1.7K]
3 years ago
8

What is the reason for each step in the solution of the equation? 18−2x=4x

Mathematics
2 answers:
Gekata [30.6K]3 years ago
6 0
You want to get all the x's on one side of the equation so add 2x to both sides of the equation. 4x + 2x = 6x. now you want to get the x by itself so dived both sides of the equation by 6. 18 = 6x, 18/6 = x, x = 3 
Reika [66]3 years ago
3 0
In order to solve an equation for a certain variable, you should isolate that variable on one side of the equation and leave all the other terms on the other side on the equation.
The, you solve to get the value of the variable.

The equation we have here is:
<span>18−2x=4x
First, we need to isolate the terms containing the "x" on one side of the equation. To do this, we will add 2x to both sides of the equation:
</span><span>18−2x+2x=4x+2x
18 = 6x
Now, we need to get the value of the "x". To do this, we will simply divide both sides of the equation by 6:
18/6 = 6x/6
3 = x .............> This is the solution of the equation</span>
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Answer:

D (12, 21); B (11, 17); C (18,28); D (42); C (8).

Step-by-step explanation:

First:

Let I represent Isabel and M represent Marie.

We know that currently, Isabel is 9 years older than Marie, or:

I=9+M.

In three years, Isabel will be six years less than twice of Marie's age. In other words:

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Second:

Let I represent Isabel and M represent Marie.

Isabel is 6 years older than Marie; in other words: I=6+M

In 4 years, Isabel will be 9 years less than twice Marie's age. Or:

(I+4)=2(M+4)-9

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(6+M+4)=2(M+4)-9

10+M=2M+8-9

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11=M; I=17; Marie is 11 while Isabel is 17.

Third:

Let I represent Isabel and M represent Marie.

Isabel is 10 years older than Marie, or: I=10+M

In 2 years, twice Isabel's age is three times Marie's age. Or:

2(I+2)=3(M+2)

Solve. Substitute for I.

2(10+M+2)=3(M+2)

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18=M; I=28. Marie is 18 while Isabel is 28.

Fourth:

Let M represent Mary and A represent Ann.

Mary is 3 time as old as Ann. Or: M=3A

7 years ago Mary was 5 times as old as Ann. In other words:

(M-7)=5(A-7)

Solve for this system. Substitute M.

(3A-7)=5A-35

-2A=-28

A=14; M=42; Mary is 42.

Fifth:

Let T represent Tammy and L represent Laurel.

We know that Tammy is 42 while Laurel is 9. In other words:

T=42 and L=9.

We need to find in how many years will 3 times Laurel's age be 1 more than Tammy's age. In other words, let's let y represent the amount of years. Thus:

3(L+y)=(T+y)+1

We already know L and T:

3(9+y)=(42+y)+1

27+3y=43+y

2y=16

y=8

In 8 years, when Laurel is 17 and Tammy is 50. (3 times 17 is 51, one more than 50).

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