Question $5 x-8=11-7 x+12 x$

Studdy Solution

STEP 1

What is this asking? Solve for $x$ in the equation $5x - 8 = 11 - 7x + 12x$ . Watch out! Don't forget to combine like terms on both sides before solving!

STEP 2

1. Simplify both sides
2. Move all terms with $x$ to one side
3. Solve for $x$

STEP 3

Alright, let's simplify the right side of the equation first.
We have $11 - 7x + 12x$ .
Notice that we have two terms with $x$ .
Let's combine them!
$11 - 7x + 12x = 11 + (12x - 7x)$

STEP 4

Now, calculate $12x - 7x$ :
$12x - 7x = 5x$ So, the right side becomes:
$11 + 5x$

STEP 5

Now, let's rewrite the equation with the simplified right side:
$5x - 8 = 11 + 5x$

STEP 6

We want to move all the terms with $x$ to one side of the equation.
Let's subtract $5x$ from both sides to make it easier to see what's happening:
$5x - 8 - 5x = 11 + 5x - 5x$

STEP 7

Simplify both sides:
$-8 = 11$

STEP 8

Oops! It looks like we made a mistake.
Let's go back and check our work.
We should have moved the constant terms to one side instead.
Let's try again:
Subtract 11 from both sides:
$5x - 8 - 11 = 5x$

STEP 9

Simplify the left side:
$5x - 19 = 5x$

STEP 10

Subtract $5x$ from both sides to isolate the constant:
$5x - 5x - 19 = 5x - 5x$

STEP 11

Simplify:
$-19 = 0$ Oh no!
It seems like we've ended up with a contradiction, which means our initial equation has no solution!

STEP 12

There is no solution for the equation $5x - 8 = 11 - 7x + 12x$ .

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