Math Snap

STEP 1

What is this asking?
We need to find the value of $x$ that makes the equation $-5x - 2(-10x - 6) + 4 = 7$ true.
Watch out!
Don't forget to distribute the $-2$ correctly to both terms inside the parentheses!

STEP 2

1. Simplify the equation
2. Isolate the $x$ term
3. Find the solution

STEP 3

Alright, let's kick things off by distributing that $-2$ to the terms inside the parentheses.
Remember, this means multiplying $-2$ by both $-10x$ and $-6$.
So, we get:
$$-5x + 20x + 12 + 4 = 7$$ Why? Because $-2 \cdot -10x = 20x$ and $-2 \cdot -6 = 12$.

STEP 4

Now, let's tidy things up a bit!
We have some like terms on the left side of the equation.
We've got $-5x$ and $20x$, and we also have $12$ and $4$.
Combining these, we get:
$$15x + 16 = 7$$ Because $-5x + 20x = 15x$ and $12 + 4 = 16$.

STEP 5

To get that $x$ term all alone, we need to subtract $16$ from both sides of the equation:
$$15x + 16 - 16 = 7 - 16$$ $$15x = -9$$Remember, we're adding $-16$ to both sides to make the $16$ on the left disappear by adding to zero.

STEP 6

Almost there!
Now, we just need to divide both sides by $15$ to isolate $x$:
$$\frac{15x}{15} = \frac{-9}{15}$$ $$x = -\frac{9}{15}$$We divide by $15$ to make the $15$ multiplying $x$ disappear by dividing to one.

STEP 7

We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is $3$:
$$x = -\frac{9 \div 3}{15 \div 3}$$ $$x = -\frac{3}{5}$$

So, the grand solution is $x = -\frac{3}{5}$!