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Chapter 8: Problem 5

Solve each equation. $$28+72+134+x=360$$

Short Answer

Expert verified
The value of \( x \) is 126.

Step by step solution

01

Understand the Equation

We are given the equation \( 28 + 72 + 134 + x = 360 \). The goal is to find the value of the variable \( x \).
02

Combine Known Terms

First, add together the known numbers on the left side of the equation. Calculate \( 28 + 72 + 134 \).
03

Perform the Addition

Calculate \( 28 + 72 = 100 \). Then, add \( 134 \) to \( 100 \), which gives us \( 234 \). Thus, the equation simplifies to \( 234 + x = 360 \).
04

Isolate the Variable \( x \)

Subtract \( 234 \) from both sides of the equation to solve for \( x \). This gives \( x = 360 - 234 \).
05

Calculate the Value of \( x \)

Calculate \( 360 - 234 \) to find \( x = 126 \).

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Key Concepts

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

Algebra
Algebra is like a magical toolbox for solving mathematical puzzles. It allows us to use letters, known as variables, to stand in for unknown numbers. In our exercise, the letter \( x \) is the variable. Our job is to find out what number \( x \) is hiding behind. We do this by using known
  • numbers
  • operations, like addition and subtraction
  • an equation to connect everything
In this specific problem, we were given the equation \( 28 + 72 + 134 + x = 360 \). The numbers \( 28, 72, \text{ and } 134 \) are called the constants. They're not changing, and they're already known. Using algebra, we will manipulate these numbers and solve for \( x \). Algebra makes finding unknowns much more structured, and it's a critical part of mathematics that you鈥檒l use often.
Solving Equations
Solving equations involves finding the value of the unknown, in this case, \( x \). Generally, an equation is a mathematical statement that asserts the equality of two expressions. In this exercise, the equation is \( 28 + 72 + 134 + x = 360 \).

Here are the steps we used to solve this equation:
  • First, we looked at the numbers we already knew: \( 28, 72, \text{and } 134 \).
  • We combined these numbers to make the equation easier to handle. We added them up step by step, first \( 28 + 72 = 100 \).
  • Next, we added \( 134 \), resulting in \( 234 \). So the equation simplified to \( 234 + x = 360 \).
Now that we've simplified the equation, it's much easier to find \( x \). This is a basic approach in algebra for tackling more complex problems in steps.
Isolation of Variables
Isolation of variables is a fancy way of saying "let's get the unknown by itself." Think of it like unwrapping a gift: you have to get all the packaging off before you see what's inside. In solving our exercise, the goal was to isolate \( x \), the unknown variable, on one side of the equation.

Here鈥檚 how we did it:
  • We started with the simplified equation: \( 234 + x = 360 \).
  • To isolate \( x \), we need to remove \( 234 \) from the left-hand side, which we can do by subtracting \( 234 \) from both sides of the equation.
  • This operation changes the equation to \( x = 360 - 234 \).
  • Finally, compute \( 360 - 234 \) to find \( x = 126 \).
By isolating \( x \), we discovered its value. This method of getting the unknown alone is a key skill because it helps us uncover what the variable represents.

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