What is the best method for Solving equations with variables on both sides?
This is the problem:
1(6x-x)=162+12x
(6x-x)=162+12x
5x = 162 + 12x
5x - 12x = 162
-7x = 162
x = ?
To solve equations with variables on both sides, follow these steps:
Step 1: Simplify both sides of the equation by performing any necessary operations, such as distributing and combining like terms.
In the given problem, start by distributing the 1 to the terms inside the parentheses:
6x - x = 162 + 12x
Simplifying further, we have:
5x = 162 + 12x
Step 2: Move all terms with variables to one side of the equation by adding or subtracting.
In this case, subtract 12x from both sides to move all the terms with x to the left side:
5x - 12x = 162 + 12x - 12x
Simplifying, we get:
-7x = 162
Step 3: Solve for x by isolating the variable.
Divide both sides of the equation by -7:
-7x / -7 = 162 / -7
This simplifies to:
x = -23.142857...
So, the solution to the equation is x = -23.142857...
Always remember to double-check your solution by substituting it back into the original equation to ensure it is correct.