Problem 35 Solve each equation, and check y... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 2: Problem 35

Solve each equation, and check your solution. $$ 8 t+6=7 t+6 $$

Short Answer

Expert verified

t = 0

Step by step solution

Move all terms involving t to one side

Subtract 7t from each side of the equation to isolate the t terms on one side. 8t + 6 - 7t = 7t + 6 - 7t This simplifies to: t + 6 = 6

Isolate t

Subtract 6 from both sides to isolate the variable t. t + 6 - 6 = 6 - 6 This simplifies to: t = 0

Check the solution

Substitute t = 0 back into the original equation to verify the solution. 8(0) + 6 = 7(0) + 6 Which simplifies to: 6 = 6 Since both sides of the equation are equal, t = 0 is a correct solution.

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Key Concepts

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

Equation Isolation

To solve linear equations, it's crucial to isolate the variable. This means getting the variable you're solving for on one side of the equation by itself. In the given equation, we have $8t + 6 = 7t + 6$.

Our goal here is to isolate $t$. We start by moving all terms involving $t$ to the same side. We do this by subtracting $7t$ from both sides:
8t + 6 - 7t = 7t + 6 - 7t
This simplifies to:
t + 6 = 6.
Now, we just need to deal with the constant term next to $t$.

Subtract 6 from both sides to get $t$ by itself:
t + 6 - 6 = 6 - 6
This simplifies to:
t = 0.
By isolating the variable, we get $t = 0$ as the solution.

Checking Solutions

After solving an equation, it's important to check your solution to make sure it's correct. Substituting the solution back into the original equation can help verify it. For the equation $8t + 6 = 7t + 6$, we found $t = 0$.

Substitute $t = 0$ back into the original equation:
8(0) + 6 = 7(0) + 6
This simplifies to:
6 = 6.
Since both sides of the equation are equal, we can confirm that our solution $t = 0$ is correct.

Always remember to perform this verification step. It ensures you haven't made any mistakes during the process and that your solution is accurate.

Simplifying Algebraic Expressions

Simplifying algebraic expressions makes solving equations easier. Simplification involves combining like terms and eliminating unnecessary constants or variables. In our example, the equation $8t + 6 = 7t + 6$ involves simplifying by moving terms to one side.

First, subtract $7t$ from both sides to combine like terms involving $t$:
8t + 6 - 7t = 7t + 6 - 7t
This simplifies to:
t + 6 = 6.
Next, subtraction is used to eliminate the constant term on the same side as $t$:
t + 6 - 6 = 6 - 6
This results in:
t = 0.
By simplifying, we reduced a potentially complex equation to a much simpler form, making it easier to solve.

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91影视

Solve each equation, and check your solution. $$ 8 t+6=7 t+6 $$

Short Answer

Step by step solution

Move all terms involving t to one side

Isolate t

Check the solution

Key Concepts

Equation Isolation

Checking Solutions

Simplifying Algebraic Expressions

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