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What is the solution for $x$ in the equation?
$10 x-4.5+3 x=12 x-1.1$
$x=\square$

Combine like terms: 10 x + 3 x − 4.5 = 13 x − 4.5 , so the equation is 13 x − 4.5 = 12 x − 1.1 .
Subtract 12 x from both sides: x − 4.5 = − 1.1 .
Add 4.5 to both sides: x = − 1.1 + 4.5 .
The solution is 3.4 ​ .

Explanation

Problem Analysis We are given the equation 10 x − 4.5 + 3 x = 12 x − 1.1 . Our goal is to solve for x . We will achieve this by simplifying the equation and isolating x on one side.

Combine Like Terms First, combine the like terms on the left side of the equation: 10 x + 3 x − 4.5 = 13 x − 4.5 .
So the equation becomes 13 x − 4.5 = 12 x − 1.1 .

Isolate x Next, subtract 12 x from both sides of the equation to get the x terms on one side: 13 x − 12 x − 4.5 = 12 x − 12 x − 1.1 , which simplifies to x − 4.5 = − 1.1 .

Solve for x Now, add 4.5 to both sides of the equation to isolate x :
x − 4.5 + 4.5 = − 1.1 + 4.5 , which simplifies to x = 3.4 .

Final Answer Therefore, the solution for x is 3.4 .


Examples
In real-world scenarios, solving linear equations like this can help determine the break-even point in business. For example, if x represents the number of units you need to sell to make revenue equal to your costs, solving the equation helps you find that critical value. Understanding how to manipulate and solve such equations is fundamental in making informed financial decisions and strategic planning.

Answered by GinnyAnswer | 2025-07-04

To solve 10 x − 4.5 + 3 x = 12 x − 1.1 , we combine like terms to simplify and isolate x . After performing the necessary arithmetic, we find that x = 3.4 .
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Answered by Anonymous | 2025-07-06