Solve the equation.
[tex]8-2 x=-8 x+14[/tex]
A. [tex]x=-1[/tex]
B. [tex]x=-\frac{3}{5}[/tex]
C. [tex]x=\frac{3}{5}[/tex]
D. [tex]x=1[/tex]
Answer (2)
Add 8 x to both sides: 8 + 6 x = 14 .
Subtract 8 from both sides: 6 x = 6 .
Divide both sides by 6: x = 1 .
The solution to the equation is 1 .
Explanation
Understanding the Problem We are given the equation 8 − 2 x = − 8 x + 14 and asked to solve for x . We will manipulate the equation to isolate x on one side.
Adding 8x to Both Sides First, we add 8 x to both sides of the equation to get the x terms on the same side: 8 − 2 x + 8 x = − 8 x + 14 + 8 x
8 + 6 x = 14
Subtracting 8 from Both Sides Next, we subtract 8 from both sides to isolate the term with x :
8 + 6 x − 8 = 14 − 8 6 x = 6
Dividing by 6 Finally, we divide both sides by 6 to solve for x :
6 6 x = 6 6 x = 1
Final Answer Therefore, the solution to the equation 8 − 2 x = − 8 x + 14 is x = 1 .
Examples
In real life, solving linear equations like this can help determine the break-even point for a business. For example, if the cost of producing x items is 8 + 2 x dollars and the revenue from selling x items is 8 x + 14 dollars, solving the equation 8 + 2 x = 8 x + 14 would tell you how many items you need to sell to break even (where cost equals revenue). In this case, you would need to sell 1 item to break even.
By rearranging and simplifying the given equation, we found that the solution is x = 1 . Therefore, the correct choice is option D. This result helps us understand how to isolate variables in algebraic equations.
;
