Solve the equation.
$8 q-6=2 q-48$
Answer (1)
Subtract 2 q from both sides: 6 q − 6 = − 48 .
Add 6 to both sides: 6 q = − 42 .
Divide both sides by 6: q = − 7 .
The solution to the equation is − 7 .
Explanation
Understanding the Equation We are given the equation 8 q − 6 = 2 q − 48 . Our goal is to isolate the variable q on one side of the equation to find its value.
Subtracting 2q from Both Sides First, let's subtract 2 q from both sides of the equation to get the terms with q on one side: 8 q − 6 − 2 q = 2 q − 48 − 2 q 6 q − 6 = − 48
Adding 6 to Both Sides Next, we add 6 to both sides of the equation to isolate the term with q :
6 q − 6 + 6 = − 48 + 6 6 q = − 42
Dividing by 6 to Solve for q Finally, we divide both sides of the equation by 6 to solve for q :
6 6 q = 6 − 42 q = − 7
Final Answer Therefore, the solution to the equation 8 q − 6 = 2 q − 48 is q = − 7 .
Examples
In real life, solving linear equations like this can help you determine how many items you need to sell to break even. For example, if your costs are represented by 2 q − 48 and your revenue is 8 q − 6 , solving for q tells you the number of items you need to sell to make your revenue equal to your costs.
