Solve. [tex]$15 t+8=4-t$[/tex]
Answer (2)
Add t to both sides of the equation: 16 t + 8 = 4 .
Subtract 8 from both sides: 16 t = − 4 .
Divide both sides by 16: t = − 16 4 .
Simplify the fraction: t = − 4 1 .
Explanation
Understanding the Problem We are given the equation 15 t + 8 = 4 − t . Our goal is to solve for t , which means we want to isolate t on one side of the equation.
Adding t to Both Sides First, let's add t to both sides of the equation to get all the t terms on one side: 15 t + 8 + t = 4 − t + t
16 t + 8 = 4
Subtracting 8 from Both Sides Next, we subtract 8 from both sides to isolate the term with t :
16 t + 8 − 8 = 4 − 8 16 t = − 4
Dividing by 16 and Simplifying Finally, we divide both sides by 16 to solve for t :
16 16 t = 16 − 4 t = − 16 4 We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4: t = − 16 ÷ 4 4 ÷ 4 t = − 4 1
Final Answer Therefore, the solution to the equation is t = − 4 1 .
Examples
Solving linear equations like this is a fundamental skill in algebra and is used in many real-world applications. For example, if you are trying to determine how many hours you need to work at a certain wage to earn a specific amount of money, you might set up a linear equation. Suppose you earn $15 per hour and have already earned $8. If you need to earn a total of $4, you can use the equation 15 t + 8 = 4 to find out how many more hours ( t ) you need to work. In this case, the solution t = − 4 1 indicates that you have already earned more than your target amount, and you don't need to work any additional hours.
To solve the equation 15 t + 8 = 4 − t , we isolated t to find that t = − 4 1 . This involved combining like terms, isolating t , and simplifying fractions. Thus, the final answer is t = − 4 1 .
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