Select the correct answer.
What is the solution for $x$ in the equation?
$16 x-4+5 x=-67$
A. $x=\frac{1}{3}$
B. $x=-3$
C. $x=-\frac{1}{3}$
D. $x=3
Answer (1)
Combine like terms: 16 x + 5 x − 4 = − 67 becomes 21 x − 4 = − 67 .
Add 4 to both sides: 21 x = − 63 .
Divide by 21: x = − 3 .
The solution is x = − 3 .
Explanation
Understanding the Problem We are given the equation 16 x − 4 + 5 x = − 67 . Our goal is to find the value of x that satisfies this equation.
Combining Like Terms First, we combine the like terms on the left side of the equation. We have 16 x and 5 x , which combine to give 21 x . So the equation becomes 21 x − 4 = − 67 .
Isolating the x Term Next, we want to isolate the term with x . To do this, we add 4 to both sides of the equation:
21 x − 4 + 4 = − 67 + 4
This simplifies to 21 x = − 63 .
Solving for x Now, we divide both sides of the equation by 21 to solve for x :
21 21 x = 21 − 63
This simplifies to x = − 3 .
Final Answer Therefore, the solution for x is − 3 . Comparing this to 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 amount of ingredients in a recipe when scaling it up or down, determining the break-even point in business, or calculating distances and speeds in physics. For example, if you know that a taxi charges a fixed fee of $4 and an additional $5 per mile, you can use a linear equation to determine how many miles you can travel for a given budget. If your budget is $67, the equation would be 5 x + 4 = 67 , where x is the number of miles. Solving for x would tell you how far you can travel.
