If $-2(2 x-11)=3(x-9)$, then $x=$
A. 2
B. 3
C. 5
D. 7
Answer (2)
Expand both sides of the equation: − 2 ( 2 x − 11 ) = − 4 x + 22 and 3 ( x − 9 ) = 3 x − 27 .
Set the expanded expressions equal: − 4 x + 22 = 3 x − 27 .
Isolate x by adding 4 x and 27 to both sides: 49 = 7 x .
Solve for x by dividing both sides by 7 : x = 7 .
Explanation
Understanding the Problem We are given the equation − 2 ( 2 x − 11 ) = 3 ( x − 9 ) and we need to find the value of x that satisfies this equation.
Expanding Both Sides First, we expand both sides of the equation: − 2 ( 2 x − 11 ) = − 4 x + 22 3 ( x − 9 ) = 3 x − 27
Setting Up the Equation Now we set the expanded expressions equal to each other: − 4 x + 22 = 3 x − 27
Isolating x Next, we want to isolate x on one side of the equation. We can add 4 x to both sides: 22 = 7 x − 27
Further Isolating x Then, we add 27 to both sides: 22 + 27 = 7 x 49 = 7 x
Solving for x Finally, we divide both sides by 7 to solve for x :
x = 7 49 x = 7
Final Answer Therefore, the value of x that satisfies the equation is 7 .
Examples
Linear equations are used in everyday life to calculate things like the cost of items, the distance traveled, and the time it takes to complete a task. For example, if you know the hourly rate you earn at a job and the total amount you earned, you can use a linear equation to find the number of hours you worked. Similarly, if you are planning a road trip and know the distance you need to travel and the average speed you will be driving, you can use a linear equation to calculate the time it will take to reach your destination. Understanding how to solve linear equations is a valuable skill that can be applied to many real-world situations.
The solution to the equation − 2 ( 2 x − 11 ) = 3 ( x − 9 ) is x = 7 . Therefore, the correct answer is option D. 7.
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