Problem 11 Solve using the addition princip... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 11: Problem 11

Solve using the addition principle. $$ -22=t+4 $$

Short Answer

Expert verified

-26

Step by step solution

Identify the Equation

The given equation is -22 = t + 4

Isolate the Variable

To isolate the variable t, we need to remove the constant term on the right side of the equation.Currently the constant term is 4, so we move it to the other side by subtracting 4 from both sides.

Subtract 4 from Both Sides

Perform the subtraction: -22 - 4 = t + 4 - 4 which simplifies to -26 = t

Solution

The value of t is -26. Therefore, t = -26.

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Key Concepts

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

addition principle

The addition principle is a key concept in algebra. It helps solve equations by balancing both sides. Think of an equation as a balanced scale. If you add or subtract the same number from each side, the scale remains balanced. This principle makes it easier to isolate variables.
In this exercise, the original equation is $-22 = t + 4$. To isolate the variable $ t $, subtract 4 from both sides:
$-22 - 4 = t + 4 - 4$. This helps maintain the balance. Simplifying gives $-26 = t$. Using the addition principle effectively, we isolated the variable to find $-26$.

isolating variables

Isolating variables is crucial in solving algebraic equations. It means getting the variable (e.g., $ t $) alone on one side of the equation. The aim is to simplify the equation to find the variable's value.
Start with the given equation, $-22 = t + 4$. To isolate $ t $, we need to remove the constant term (4). We do this by performing the inverse operation鈥攕ubtracting 4 from both sides. This results in $-22 - 4 = t + 4 - 4$.
Simplifying this gives $-26 = t$. Now the variable $ t $ is isolated, making it easy to see that $ t = -26$.

basic algebra

Basic algebra involves operations like addition, subtraction, multiplication, and division to solve equations. The goal is often to find the value of an unknown variable.
In our exercise, we started with $-22 = t + 4$. Utilizing basic algebraic techniques, we aimed to isolate $ t $ by eliminating the constant (4).
We did this by subtracting 4 from both sides, resulting in $-22 - 4 = t + 4 - 4$ which simplifies to $-26 = t$. This straightforward subtraction is a fundamental algebraic step. Finally, by simplifying the equation, we found that $ t = -26$, demonstrating the power of basic algebra in solving linear equations.

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91影视

Solve using the addition principle. $$ -22=t+4 $$

Short Answer

Step by step solution

Identify the Equation

Isolate the Variable

Subtract 4 from Both Sides

Solution

Key Concepts

addition principle

isolating variables

basic algebra

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