Solve the equation for $x$.
$\frac{1}{2}(x-3)-10=-2$
Answer (2)
Add 10 to both sides: 2 1 ( x − 3 ) = 8 .
Multiply both sides by 2: x − 3 = 16 .
Add 3 to both sides: x = 19 .
The solution is 19 .
Explanation
Understanding the Problem We are given the equation 2 1 ( x − 3 ) − 10 = − 2 and we want to solve for x . Let's break it down step by step.
Isolating the Term with x First, we want to isolate the term with x . We can do this by adding 10 to both sides of the equation: 2 1 ( x − 3 ) − 10 + 10 = − 2 + 10 2 1 ( x − 3 ) = 8
Removing the Fraction Next, we want to get rid of the fraction. We can do this by multiplying both sides of the equation by 2: 2 ⋅ 2 1 ( x − 3 ) = 2 ⋅ 8 x − 3 = 16
Isolating x Now, we want to isolate x . We can do this by adding 3 to both sides of the equation: x − 3 + 3 = 16 + 3 x = 19
Final Answer Therefore, the solution to the equation is x = 19 .
Examples
Imagine you're baking a cake and need to adjust the recipe. If the original recipe feeds too many people, you can use similar algebraic steps to scale down the ingredients proportionally. For example, if you halve the recipe and then realize you need to add a bit more of an ingredient, you're essentially solving an equation to find the adjusted amount. This kind of problem-solving is useful in cooking, construction, and many other fields where you need to adjust quantities based on a set of conditions.
To solve the equation 2 1 ( x − 3 ) − 10 = − 2 , we first add 10 to both sides to isolate the fraction, then multiply by 2 to remove it, and finally add 3 to solve for x . The solution is x = 19 .
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