Solve the equation for $x$. $1=1-5x-7x$
Answer (2)
Combine like terms: 1 = 1 − 12 x .
Subtract 1 from both sides: 0 = − 12 x .
Divide by -12: x = 0 .
The solution is 0 .
Explanation
Problem Analysis We are given the equation 1 = 1 − 5 x − 7 x and asked to solve for x . Our goal is to isolate x on one side of the equation.
Combining Like Terms First, we combine the like terms on the right side of the equation: 1 = 1 − 5 x − 7 x
1 = 1 − 12 x
Isolating the x Term Next, we subtract 1 from both sides of the equation to further isolate the term with x :
1 − 1 = 1 − 12 x − 1 0 = − 12 x
Solving for x Now, we divide both sides of the equation by -12 to solve for x :
− 12 0 = − 12 − 12 x 0 = x
Final Answer Therefore, the solution to the equation is x = 0 .
Examples
In real-world scenarios, solving linear equations like this can help determine break-even points in business. For example, if a business's revenue is represented by 1 and its costs are represented by 1 − 5 x − 7 x , finding the value of x that makes these equal (i.e., solving the equation) tells the business the point at which they neither make nor lose money. This is a fundamental concept in financial analysis and decision-making.
The solution to the equation 1 = 1 − 5 x − 7 x is x = 0 . We combined the like terms and isolated x to reach this conclusion. Therefore, the value of x that satisfies the equation is zero.
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