Solve the equation. Express numbers in simplest form.
[tex]$-2 a+78=24$[/tex]
Answer (2)
To solve the equation − 2 a + 78 = 24 , we subtract 78 from both sides to isolate − 2 a , then divide by -2 to find a = 27 . Checking the solution confirms its accuracy as it satisfies the original equation. The final answer is {27}.
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Subtract 78 from both sides of the equation: − 2 a = 24 − 78 , which simplifies to − 2 a = − 54 .
Divide both sides by -2: a = − 2 − 54 .
Simplify to find the value of a : a = 27 .
The solution set is 27 .
Explanation
Understanding the Problem We are given the equation − 2 a + 78 = 24 and our goal is to find the value of a that makes this equation true. To do this, we need to isolate a on one side of the equation.
Isolating the Term with 'a' First, we subtract 78 from both sides of the equation to get the term with a by itself: − 2 a + 78 − 78 = 24 − 78
− 2 a = − 54
Solving for 'a' Next, we divide both sides of the equation by -2 to solve for a : − 2 − 2 a = − 2 − 54
a = 27
Checking the Solution Therefore, the solution to the equation is a = 27 . We can check our answer by substituting a = 27 back into the original equation: − 2 ( 27 ) + 78 = − 54 + 78 = 24
Since this is true, our solution is correct.
Final Answer The solution set is {27}.
Examples
Imagine you're managing a budget. You start with $78, but after spending some amount (represented by 2 times 'a'), you're left with $24. Solving this equation helps you determine exactly how much money you spent. This kind of problem is useful in personal finance, business, and accounting, where you need to track income and expenses to manage resources effectively.
