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 will first simplify both sides of the equation using the properties of operations.
First, let's group all the x terms on one side of the equation and the constant terms on the other side by subtracting 2x from both sides:
2x - 2x - 5 = 8x - 2x + 7
Simplifying, we have:
-5 = 6x + 7
Next, let's isolate the x term by subtracting 7 from both sides to move the constant term:
-5 - 7 = 6x + 7 - 7
-12 = 6x
Now, let's solve for x by dividing both sides by 6:
-12/6 = 6x/6
-2 = x
Therefore, x = -2 is the solution to the equation 2x - 5 = 8x + 7.
We can verify this solution by substituting x = -2 back into the original equation:
2(-2) - 5 = 8(-2) + 7
-4 - 5 = -16 + 7
-9 = -9
Since both sides of the equation are equal, we can conclude that x = -2 is the correct solution.