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Chapter 11: Problem 20

Solve using the addition principle. $$ t-5=12 $$

Short Answer

Expert verified
t = 17

Step by step solution

01

Identify the variable and the equation

The given equation is \(t - 5 = 12\). The goal is to solve for the variable \(t\).
02

Apply the Addition Principle

To isolate the variable \(t\), add 5 to both sides of the equation: \(t - 5 + 5 = 12 + 5\). This balances the equation and helps to maintain equality on both sides.
03

Simplify both sides

Simplify the left and right sides of the equation: \(t = 17\). This gives the value of the variable \(t\).

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Key Concepts

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

solving equations
Solving equations is a fundamental skill in algebra. It involves finding the value of the unknown variable that makes the equation true.
To solve an equation like \( t - 5 = 12 \), follow these steps:
  • Identify the variable and any constants
  • Use mathematical operations to balance and simplify the equation
  • Check your solution by substituting it back into the original equation

Here, we identify that \( t \) is the variable, and \( -5 \) and \( 12 \) are constants. The goal is to find the value of \( t \) that satisfies the equation.
variable isolation
Variable isolation is the process of manipulating an equation to get the variable alone on one side of the equation. This often involves:
  • Adding or subtracting terms on both sides
  • Multiplying or dividing both sides by a constant

In our given equation \( t - 5 = 12 \), we want to isolate \( t \). To do this, use the addition principle by adding \( 5 \) to both sides: \[ t - 5 + 5 = 12 + 5 \].
This step ensures that the \( -5 \) on the left side is canceled out, leaving \( t \) alone.
basic algebra
Basic algebra involves understanding and applying simple algebraic operations and principles. Key operations include:
  • Adding and subtracting
  • Multiplying and dividing
  • Using the distributive property

In the context of our equation \( t - 5 = 12 \):
  • We used addition to cancel out the \( -5 \) term
  • We then simplified both sides, leading to \( t = 17 \)

Understanding these basic principles helps in solving more complex algebraic equations.

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