Select the correct answer.
Which value of [tex]$x$[/tex] makes this equation true?
[tex]$-12 x-2(x+9)=5(x+4)$[/tex]
A. -2
B. 5
C. [tex]$-\frac{1}{3}$[/tex]
D. [tex]$\frac{13}{19}$[/tex]
Answer (1)
Expand both sides of the equation: − 12 x − 2 x − 18 = 5 x + 20 .
Combine like terms: − 14 x − 18 = 5 x + 20 .
Isolate the x term: − 38 = 19 x .
Solve for x: x = − 2 .
Explanation
Problem Analysis We are given the equation − 12 x − 2 ( x + 9 ) = 5 ( x + 4 ) and asked to find the value of x that makes the equation true. We will solve this equation step-by-step.
Expanding the Equation First, we expand both sides of the equation: − 12 x − 2 x − 18 = 5 x + 20
Combining Like Terms Next, we combine like terms on the left side of the equation: − 14 x − 18 = 5 x + 20
Isolating x Terms Now, we want to isolate the x terms on one side of the equation. We can add 14 x to both sides: − 14 x − 18 + 14 x = 5 x + 20 + 14 x − 18 = 19 x + 20
Isolating the x Term Subtract 20 from both sides to isolate the x term: − 18 − 20 = 19 x + 20 − 20 − 38 = 19 x
Solving for x Finally, we solve for x by dividing both sides by 19: 19 − 38 = 19 19 x x = − 2
Checking the Answer We can check our answer by substituting x = − 2 into the original equation: − 12 ( − 2 ) − 2 ( − 2 + 9 ) = 5 ( − 2 + 4 ) 24 − 2 ( 7 ) = 5 ( 2 ) 24 − 14 = 10 10 = 10 Since the equation holds true, our solution is correct.
Final Answer The value of x that makes the equation true is x = − 2 . Therefore, the correct answer is A.
Examples
Linear equations are used in various real-life scenarios, such as calculating the cost of items with discounts or taxes, determining the distance traveled at a constant speed, or converting between different units of measurement. For example, if you want to buy a shirt that costs $25 and is on sale for 20% off, you can use a linear equation to calculate the final price. Similarly, if you are driving at a constant speed of 60 miles per hour, you can use a linear equation to determine how far you will travel in a given amount of time. Understanding how to solve linear equations is a fundamental skill that can be applied to many practical situations.
