Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
7(x+4) = 5(x+2)
To solve the equation 7(x+4) = 5(x+2), we can use the distributive property.
Applying the distributive property to the left side of the equation:
7(x+4) = 7*x + 7*4 = 7x + 28
Applying the distributive property to the right side of the equation:
5(x+2) = 5*x + 5*2 = 5x + 10
Now the equation becomes:
7x + 28 = 5x + 10
To solve for x, we need to isolate the variable on one side of the equation. We can do this by using the subtraction property of equality. By subtracting 5x from both sides of the equation, we get:
7x - 5x + 28 = 5x - 5x + 10
Simplifying the equation:
2x + 28 = 10
Next, we can use the subtraction property of equality again to isolate the constant term. By subtracting 28 from both sides of the equation, we get:
2x + 28 - 28 = 10 - 28
Simplifying the equation:
2x = -18
Finally, we can solve for x by dividing both sides of the equation by 2:
(2x)/2 = (-18)/2
Simplifying the equation:
x = -9
Therefore, the solution to the equation 7(x+4) = 5(x+2) is x = -9.