Select the correct answer.
Solve for $x$.
$10(2 x-4)=100 x$
A. $x=\frac{1}{2}$
B. $x=-\frac{1}{2}$
C. $x=3$
D. $x=7$
Answer (1)
Distribute the constant: 10 ( 2 x − 4 ) = 20 x − 40 .
Rewrite the equation: 20 x − 40 = 100 x .
Isolate x: − 40 = 80 x .
Solve for x: x = − 2 1 .
Explanation
Understanding the problem We are given the equation 10 ( 2 x − 4 ) = 100 x and we need to solve for x .
Distributing the constant First, distribute the 10 on the left side of the equation: 10 ( 2 x − 4 ) = 10 × 2 x − 10 × 4 = 20 x − 40 So the equation becomes: 20 x − 40 = 100 x
Isolating x terms Next, we want to isolate the terms with x on one side of the equation. Subtract 20 x from both sides: 20 x − 40 − 20 x = 100 x − 20 x − 40 = 80 x
Solving for x Now, solve for x by dividing both sides by 80: 80 − 40 = 80 80 x x = − 80 40 = − 2 1
Final Answer Therefore, the solution is x = − 2 1 . Comparing this with the given options, we see that option B is the correct answer.
Examples
Solving linear equations like this is fundamental in many areas, such as calculating the required dosage of medicine. For example, a pharmacist might use a linear equation to determine the amount of a drug to administer based on a patient's weight and the drug's concentration. If x represents the dosage, the equation could be set up to ensure the correct amount is given to avoid under or overdosing, making this skill crucial for accurate and safe medical practices.
