Solve the following equation, explaining what you did in each step of your solution. After solving the equation, show the steps to check your solution.
3
x
+
2
(
4
+
6
x
)
=
113
To solve the equation, we need to simplify both sides and isolate the variable x.
Step 1: Distribute the 2 to the terms inside the parentheses:
3x + 8 + 12x = 113
Step 2: Combine like terms on the left side of the equation:
15x + 8 = 113
Step 3: Subtract 8 from both sides of the equation:
15x = 105
Step 4: Divide both sides of the equation by 15:
x = 7
To check the solution, we plug x = 7 back into the original equation and see if it satisfies the equation.
3(7) + 2(4 + 6(7)) = 113
Simplifying the right side:
3(7) + 2(46) = 113
21 + 92 = 113
The left side is equal to the right side, so our solution of x = 7 is correct.