Math  /  Algebra

Question3x+327x=2(5x+10)-3 x+32-7 x=-2(5 x+10)

Studdy Solution

STEP 1

What is this asking? We need to find the value of xx that makes this equation true! Watch out! Don't forget to distribute correctly, especially with that 2-2 on the right side.
It's easy to mess up the signs!

STEP 2

1. Simplify both sides
2. Isolate the xx terms
3. Solve for xx

STEP 3

We've got 3x-3x and 7x-7x.
Combining these gives us 3x7x=10x-3x - 7x = -10x.
So, the left side becomes 10x+32-10x + 32.

STEP 4

We need to distribute the 2-2 to both terms inside the parentheses. 25x=10x-2 \cdot 5x = -10x and 210=20-2 \cdot 10 = -20.
So, the right side simplifies to 10x20-10x - 20.

STEP 5

Now, our equation looks like this: 10x+32=10x20-10x + 32 = -10x - 20.

STEP 6

To get all the xx terms on one side, let's add 10x10x to both sides of the equation.
This gives us 32=2032 = -20.

STEP 7

Whoa, the xx terms disappeared!
We had 10x-10x on both sides, and when we added 10x10x to both sides, they added to zero, leaving us with no xx terms at all!

STEP 8

We're left with 32=2032 = -20.
This is a false statement! 3232 is definitely *not* equal to 20-20.

STEP 9

Since our equation simplifies to a false statement, there's **no value of** xx that will ever make the original equation true.
That means there's **no solution**!

STEP 10

There is no solution to this equation.

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