Three times a number minus ten is equal to the sum of twice the same number and five. The equation below represents the situation. [tex]$3 x-10=2 x+5$[/tex] What is the value of [tex]$x$[/tex]?
Answer (2)
To find the value of x in the equation 3 x − 10 = 2 x + 5 , we isolate x by first subtracting 2 x from both sides and then adding 10 . The solution is x = 15 .
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Subtract 2 x from both sides: 3 x − 2 x − 10 = 2 x − 2 x + 5 , which simplifies to x − 10 = 5 .
Add 10 to both sides: x − 10 + 10 = 5 + 10 .
Simplify to find the value of x : x = 15 .
The solution to the equation is 15 .
Explanation
Understanding the Problem We are given the equation 3 x − 10 = 2 x + 5 and asked to find the value of x that satisfies it. This is a linear equation, and we can solve it by isolating x on one side of the equation.
Isolating x First, let's subtract 2 x from both sides of the equation to get all the x terms on one side:
3 x − 10 − 2 x = 2 x + 5 − 2 x
This simplifies to:
x − 10 = 5
Solving for x Now, let's add 10 to both sides of the equation to isolate x :
x − 10 + 10 = 5 + 10
This simplifies to:
x = 15
Final Answer Therefore, the value of x that satisfies the equation is 15.
Examples
Imagine you're trying to balance your monthly budget. You have some income (represented by 'x') and some expenses. The equation 3 x − 10 = 2 x + 5 could represent a simplified scenario where you're trying to figure out how much income you need to cover your expenses and have a certain amount left over. Solving this equation helps you determine the exact income ('x') required to make your budget work. Understanding and solving such equations is crucial for managing personal finances, making investment decisions, and planning for the future.
