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Chapter 2: Problem 28

Solve using the addition principle. Don't forget to check! $$ 15=-8+z $$

Short Answer

Expert verified
z = 23

Step by step solution

01

Identify the equation structure

The given equation is 15 = -8 + z
02

Apply the addition principle

According to the addition principle, add 8 to both sides of the equation to isolate the variable z. 15 + 8 = -8 + z + 8
03

Simplify the equation

Simplify both sides of the equation. 15 + 8 = 23 -8 + 8 + z = z So the simplified equation is 23 = z
04

Verify the solution

Substitute z with 23 in the original equation to check if both sides are equal. 15 = -8 + 23 Simplify the right side: 15 = 15 Since both sides are equal, the solution is correct.

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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 that allows us to find the value of unknown variables. In the given exercise, the equation to solve is: \(15 = -8 + z\).
To solve this, we need to determine the value of \(z\) that makes the equation true. This process involves manipulating the equation using various algebraic principles to isolate \(z\) on one side of the equation. This leads us to the next key concept, the addition principle, which is a useful technique for this.
isolation of variable
Isolation of a variable means rearranging the equation so that the unknown variable appears by itself on one side of the equation.
In the exercise, we isolate \(z\) by using the addition principle.
  • First, identify the equation structure: \(15 = -8 + z\).
  • Next, apply the addition principle to both sides: \(15 + 8 = -8 + z + 8\).
By adding 8 to both sides, we cancel out the \(-8\) on the right and bring \(z\) alone on one side.
Simplifying both sides gives us \(23 = z\). Now \(z\) is isolated, and we know \(z = 23\).
verifying solutions
After finding a solution, it's essential to verify it to ensure correctness. Verification involves substituting the found value back into the original equation and checking if both sides are equal. In our exercise, substitute \(z = 23\) back into the initial equation: \(15 = -8 + 23\).
Simplifying the right side gives: \(15 = 15\), which is a true statement.
  • By verifying, we confirm that our solution is correct.
    This step proves that the operations we performed to isolate \ z\ were accurate and that \ z = 23\ is the valid solution to the original equation.

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