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Does this equation have one, many, or no solutions?
2+4(3-4x)=5x+9 If one, what is the value of 'x'? Show work please.

2 Answers

5 votes

Answer:

-5x + -5 + 5x-.1

Explanation:

User Thisdotutkarsh
by
5.5k points
4 votes

Answer: This equation has one solution.

Steps:

2+4(3-4x) = 5x +9

First, we need to distribute to the terms inside the parentheses.

4 * 3 = 12 and 4 * -4= -16x

Our equation now looks like this:

2 + 12 - 16x = 5x + 9

We can now combine like terms. We have 2 like terms that we can combine:

2 + 12 + = 14

Our equation now looks like this:

-16x + 14 = 5x + 9

We can now use inverse operations to get rid of 5x. The inverse operation for addition is subtraction; so we subtract 5x on both sides. Remember, our goal is to isolate the x.

-16x + 14 = 5x + 9

-5x -5x

The fives cancel out. Our equation now looks like this:

-21x + 14 = 9

We can now use inverse operations to get rid of the 14:

-21x + 14 = 9

- 14 -14

The fourteens cancel out. Our equation now looks like this:

-21x = -5

Last step! Now we use inverse operations to isolate the x. -21 is being multiplied by x; the inverse operation for multiplication is division.

-21x/-21 = and -5/-21 = 5/21

x is equal to 5/21.

Hope this helps!

User Umakant Mane
by
5.3k points