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In Mathematics / College | 2025-07-07

Select the correct answer.

What is the solution for $x$ in the equation?
$-4+5 x-7=10+3 x-2 x$
A. $x=\frac{21}{4}$
B. $x=\frac{4}{13}$
C. $x=\frac{4}{21}$
D. $x=\frac{13}{4}$

Asked by swornali17

Answer (1)

Combine like terms on both sides of the equation: 5 x − 11 = 10 + x .
Isolate the x terms by subtracting x from both sides and adding 11 to both sides: 4 x = 21 .
Solve for x by dividing both sides by 4: x = 4 21 ​ .
The solution for x is 4 21 ​ ​ .

Explanation

Analyze the problem We are given the equation − 4 + 5 x − 7 = 10 + 3 x − 2 x and we need to find the value of x that satisfies this equation. Our first step is to simplify the equation by combining like terms on both sides.

Combine like terms First, let's combine the constant terms on the left side of the equation: − 4 − 7 = − 11 . So the left side becomes 5 x − 11 . Now, let's combine the x terms on the right side of the equation: 3 x − 2 x = x . So the right side becomes 10 + x . Now our equation looks like this: 5 x − 11 = 10 + x .

Isolate x terms Next, we want to isolate the x terms on one side of the equation and the constant terms on the other side. To do this, we can subtract x from both sides: 5 x − x − 11 = 10 + x − x , which simplifies to 4 x − 11 = 10 . Now, we add 11 to both sides: 4 x − 11 + 11 = 10 + 11 , which simplifies to 4 x = 21 .

Solve for x Finally, to solve for x , we divide both sides of the equation by 4: 4 4 x ​ = 4 21 ​ , which gives us x = 4 21 ​ .

Final Answer Therefore, the solution for x in the equation − 4 + 5 x − 7 = 10 + 3 x − 2 x is x = 4 21 ​ . Comparing this to the given options, we see that option A is the correct answer.


Examples
Imagine you are trying to balance a budget. On one side, you have expenses represented by − 4 + 5 x − 7 , where x is the number of items you buy. On the other side, you have income represented by 10 + 3 x − 2 x . Solving the equation − 4 + 5 x − 7 = 10 + 3 x − 2 x helps you determine the value of x (the number of items) for which your expenses equal your income, allowing you to balance your budget. This type of problem is a linear equation, and solving it helps in various real-life situations involving balancing quantities.

Answered by GinnyAnswer | 2025-07-07

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