Problem 53 Solve each equation, and check y... [FREE SOLUTION]

Chapter 2: Problem 53

Solve each equation, and check your solution. $$ 5 t+3+2 t-6 t=4+12 $$

Short Answer

Expert verified

t = 13

Step by step solution

Combine Like Terms

First, combine the like terms on the left side of the equation: \[5t + 2t - 6t + 3 - 6t = 4 + 12\]. This simplifies to \[t + 3 = 16\]

Isolate the Variable

Subtract 3 from both sides to isolate the variable t: \[t + 3 - 3 = 16 - 3\]. This simplifies to \[t = 13\]

Check the Solution

Substitute t back into the original equation to verify the solution: \[5(13) + 3 + 2(13) - 6(13) = 4 + 12\]. Calculate each term: \[(65 + 3 + 26 - 78) = 16\]. Since both sides are equal, \[t = 13\] is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combining Like Terms

When solving linear equations, combining like terms is a crucial step. 'Like terms' are terms that have the same variable raised to the same power. In our exercise, we start with the equation: 5t + 3 + 2t - 6t = 4 + 12. To simplify it, we combine all the terms with 't' and the constant terms separately. Let's see how it's done: 5t + 2t - 6t + 3 = 4 + 12. To combine the like terms, just add or subtract the coefficients (the numbers in front of 't'). So, 5t + 2t - 6t = t. Now, our equation looks like this: t + 3 = 16. See how much simpler it is now? Always group and combine your like terms first. It makes it easier to solve the rest of the equation.

Isolating the Variable

Once like terms are combined, the next step is isolating the variable, which means getting the variable by itself on one side of the equation. Starting with: t + 3 = 16, we want to isolate 't'. To do this, we need to get rid of the '+ 3' that's with the 't'. We do this by doing the opposite operation, which is subtraction. So, subtract 3 from both sides: t + 3 - 3 = 16 - 3, which simplifies to: t = 13. Now the variable 't' is isolated, and we have our solution: t = 13. Isolating the variable helps us find the value that makes the equation true.

Checking the Solution

The final step in solving an equation is checking the solution. This ensures that our solution is correct. To check the solution, we substitute the value of the variable back into the original equation. Let's see how it's done: The original equation is: 5t + 3 + 2t - 6t = 4 + 12. We found t = 13. Now substitute 13 for 't' in the equation: 5(13) + 3 + 2(13) - 6(13) = 4 + 12. This simplifies to: 65 + 3 + 26 - 78 = 16, which is: 16 = 16. Since both sides of the equation are equal, our solution is correct. Always check your answers to ensure accuracy and build your confidence in solving equations.

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91影视

Solve each equation, and check your solution. $$ 5 t+3+2 t-6 t=4+12 $$

Short Answer

Step by step solution

Combine Like Terms

Isolate the Variable

Check the Solution

Key Concepts

Combining Like Terms

Isolating the Variable

Checking the Solution

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