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 will apply the distributive property and then use the properties of operations to simplify and solve for x.
First, we will apply the distributive property to both sides of the equation:
7(x+4) = 5(x+2)
7*x + 7*4 = 5*x + 5*2
7x + 28 = 5x + 10
Next, we will simplify the equation by combining like terms:
7x + 28 = 5x + 10
To isolate the variable x, we will use the properties of operations to move all terms with x to one side of the equation and all constant terms to the other side.
Subtract 5x from both sides of the equation:
7x + 28 - 5x = 5x + 10 - 5x
(7x - 5x) + 28 = 10
Combine like terms:
2x + 28 = 10
To isolate the constant term, we will use the properties of operations to move the constant term to the other side of the equation.
Subtract 28 from both sides:
2x + 28 - 28 = 10 - 28
2x = -18
Finally, we will solve for x by dividing both sides of the equation by 2:
(2x) / 2 = -18 / 2
x = -9
Therefore, the solution to the equation 7(x+4) = 5(x+2) is x = -9.