Answer:
x = -24/7 or x = -3 3/7
Step-by-step explanation:
In this equation, the first thing we will do is to get rid of the denominators -- they complicate everything. So, we can multiply the entire equation by 10, since 10 is the lowest common multiple of 5 and 2, which are the denominators.
Then, the equation will look like this:
2(4x-2) + 5(1) = 5(3x+7) - 10(1)
Notice that the denominators will no longer exist.
Now, distribute on both sides of the equation.
The equation will look like this now:
8x - 4 + 5 = 15x + 35 - 10
Then, we must combine like terms. We want to isolate the variable x on one side of the equation. Let's isolate it on the right side. So, subtract 8x from both sides. The equation will look like this now: - 4 + 5 = 7x + 35 - 10
Now that x is on one side, let's move all the other terms to the left side. Subtract 25 from both sides (35 - 10 = 25 on the right side, get rid of it by subtracting 25). The equation now looks like this: - 4 + 5 - 25 = 7x
Finally, combine all on the left side.
Final equation: -24 = 7x
Now, we know 7x = -24. We want to solve for the value of x. So, divide both sides by 7.
x = -24/7 or x = -3 3/7
