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 we need to solve for x .
Combining Like Terms First, 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, subtract 1 from both sides of the equation to isolate the term with x :
1 − 1 = 1 − 1 − 12 x 0 = − 12 x
Solving for x Now, divide both sides by -12 to solve for x :
− 12 0 = − 12 − 12 x 0 = x
Final Answer Therefore, the solution is x = 0 . Comparing this to the given options, we see that option B is the correct answer.
Examples
In real-world scenarios, solving linear equations like this can help determine break-even points in business. For example, if a company's profit is modeled by P = R − C , where P is profit, R is revenue, and C is costs, solving for when P = 0 (break-even) involves solving a linear equation. Similarly, in physics, determining the time it takes for an object to reach a certain position under constant acceleration often involves solving linear equations.
The solution to the equation 1 = 1 − 5 x − 7 x is x = 0 . This was found by combining like terms and isolating the variable. Thus, the final answer is 0 .
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