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Chapter 4: Problem 49

Solve. $$ x+17.5=29.15 $$

Short Answer

Expert verified
x = 11.65

Step by step solution

01

- Isolate the variable

To solve for the variable x, start by isolating x on one side of the equation. To do that, subtract 17.5 from both sides of the equation.
02

- Perform the subtraction

Subtract 17.5 from both sides: \[ x + 17.5 - 17.5 = 29.15 - 17.5 \] This simplifies to: \[ x = 29.15 - 17.5 \]
03

- Calculate the result

Perform the subtraction on the right side: \[ x = 29.15 - 17.5 \] \[ x = 11.65 \]

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Key Concepts

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

Isolate the Variable in Algebraic Equations
When solving basic equations, one of the first steps is to isolate the variable. This means getting the unknown variable (often represented by 'x') alone on one side of the equation. If the variable you're solving for is added to another number, subtract that number from both sides. If the variable is multiplied by a number, divide both sides by that number. By doing this, you can focus on finding the actual value of the variable.
In this exercise, the goal is to solve for x in the equation: \[ x + 17.5 = 29.15 \]
The process of isolating x involves removing the 17.5 that is added to it. To do that, you need to perform subtraction on both sides of the equation.
Perform Subtraction to Solve Equations
Subtraction is a key operation in algebra, especially when isolating variables. When you see an equation where the variable is added to a number, you need to perform subtraction to move that number to the other side of the equation.
Here's how you do it: Starting with the equation: \[ x + 17.5 = 29.15 \]
Subtract 17.5 from both sides to isolate x: \[ x + 17.5 - 17.5 = 29.15 - 17.5 \]
This simplifies to: \[ x = 29.15 - 17.5 \]
By subtracting 17.5 from both sides, you've effectively moved it away from x, leaving x isolated and ready for the next step.
Basic Algebra Concepts
Basic algebra involves learning how to manipulate equations to find the value of unknown variables. One of the fundamental operations in algebra is combining like terms and using operations such as addition, subtraction, multiplication, and division.
In solving equations, always remember these key points:
  • Perform the same operation on both sides of the equation.
  • Combine like terms to simplify the equation.
In our exercise, after you subtract 17.5 from both sides, you are left with a simple subtraction: \[ x = 29.15 - 17.5 \]
Now, your task is to simplify the right-hand side:
Perform the calculation: \[ x = 11.65 \]
You've now solved the equation, and the value of x is 11.65. Understanding these basic algebra steps helps you tackle more complex equations later on.

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