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.
First, distribute 7 to both terms inside the parentheses:
7(x) + 7(4) = 5(x) + 5(2)
This simplifies to:
7x + 28 = 5x + 10
Now, we can combine like terms.
Subtract 5x from both sides of the equation:
7x + 28 - 5x = 5x + 10 - 5x
This simplifies to:
2x + 28 = 10
Next, subtract 28 from both sides of the equation to isolate the variable term:
2x + 28 - 28 = 10 - 28
This simplifies to:
2x = -18
Finally, divide both sides of the equation by 2 to solve for x:
2x / 2 = -18 / 2
This simplifies to:
x = -9
Therefore, the solution to the equation is x = -9.