Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
2x - 5 = 8x + 7
To solve the equation 2x - 5 = 8x + 7, we can start by simplifying the equation using the properties of operations.
First, we can simplify the equation by combining like terms on both sides of the equation.
On the left side, the only like term is 2x, so we can leave it as 2x.
On the right side, the only like term is 8x. To simplify the equation, we can subtract 8x from both sides of the equation. This gives us:
2x - 5 - 8x = 8x + 7 - 8x
-6x - 5 = 7
Next, we can isolate the variable x by getting rid of the constant term on the left side. To do this, we can add 5 to both sides of the equation. This gives us:
-6x - 5 + 5 = 7 + 5
-6x = 12
Now, we can solve for x by dividing both sides of the equation by -6.
-6x / -6 = 12 / -6
x = -2
Therefore, the solution to the equation 2x - 5 = 8x + 7 is x = -2.
We've used the properties of operations such as combining like terms (2x and 8x) and getting rid of constant terms (-5 and 7) to simplify the equation, isolate the variable, and solve for x.