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What is the solution for $x$ in the equation?
$10 x-4.5+3 x=12 x-1.1$
$x=\square$
Answer (1)
Combine like terms: 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
Understanding the Problem We are given the equation 10 x − 4.5 + 3 x = 12 x − 1.1 and we want to find the value of x that satisfies this equation.
Combining Like Terms First, we combine 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 .
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
Imagine you're balancing a budget. On one side, you have expenses represented by 12 x − 1.1 , and on the other side, you have income and savings represented by 10 x − 4.5 + 3 x . Solving this equation helps you find the value of x that makes your income and savings equal to your expenses, ensuring a balanced budget. This type of problem is a fundamental concept for financial planning and resource allocation.
