Type the correct answer in the box. Use numerals instead of words. What is the solution for $x$ in the equation? [tex]10 x-4.5+3 x=12 x-1.1[/tex] [tex]x=[/tex]
Answer (2)
Combine like terms: 10 x + 3 x − 4.5 = 13 x − 4.5 .
Rewrite the equation: 13 x − 4.5 = 12 x − 1.1 .
Isolate x: x = − 1.1 + 4.5 .
Solve for x: 3.4 .
Explanation
Understanding the equation We are given the equation 10 x − 4.5 + 3 x = 12 x − 1.1 and we want to solve for x .
Combining like terms First, we combine like terms on the left side of the equation: 10 x + 3 x = 13 x . So the equation becomes 13 x − 4.5 = 12 x − 1.1 .
Isolating x Next, we want to isolate x on one side of the equation. We can subtract 12 x from both sides: 13 x − 12 x − 4.5 = 12 x − 12 x − 1.1 , which simplifies to x − 4.5 = − 1.1 .
Solving for x Now, we add 4.5 to both sides of the equation to solve for 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, the equation could represent the point where your costs equal your revenue. Solving for x tells you how many units you need to sell to break even. Understanding how to manipulate and solve these equations is crucial for making informed financial decisions.
The solution for x in the equation 10 x − 4.5 + 3 x = 12 x − 1.1 is 3.4 . This was achieved by combining like terms and isolating x through simple algebraic manipulations.
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