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Chapter 2: Problem 29

Solve each equation. $$c+31-10=46$$

Short Answer

Expert verified
c = 25.

Step by step solution

01

Simplify the Equation

Simplify the left-hand side of the equation by combining the numeric terms. The equation is initially given as \[c + 31 - 10 = 46\]. Combine the terms 31 and -10:\[c + 21 = 46\].
02

Isolate the Variable

To solve for \(c\), isolate the variable by subtracting 21 from both sides of the equation:\[c + 21 - 21 = 46 - 21\].This simplifies to:\[c = 25\].

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Key Concepts

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

simplifying equations
In algebra, we often need to simplify equations to easily solve them. Simplifying means reducing an equation to its simplest form without changing its value.
To simplify, combine like terms. Like terms are terms that have the same variable raised to the same power. In the example:
  • Original equation: \[c + 31 - 10 = 46\]
  • Simplified equation: \[c + 21 = 46\]
Here, 31 and -10 are combined to make 21. When you simplify, keep the equation balanced. Do this by applying the operations to both sides.
isolating variables
To solve for a variable means to isolate it on one side of the equation.
The goal is to have the variable alone on one side and constants on the other. In our example we isolate \c\ as follows:
  • Original simplified equation: \[c + 21 = 46\]
    • ,
  • subtract 21 from both sides:\[c + 21 - 21 = 46 - 21\]
This balances the equation and simplifies to:\[c = 25\]
Isolating variables involves using inverse operations, like addition and subtraction, multiplication and division, to move terms around.
basic arithmetic operations
Solving linear equations requires the use of basic arithmetic operations:
  • Addition
  • Subtraction
  • Multiplication
  • Division
    In our given problem we use:
    • Addition:31 - 10 to get 21
    • Subtraction:46 - 21 to get 25
    Operations should be performed carefully to maintain the balance of the equation. Each operation is selected according to what is necessary to isolate the variable.
    Whenever you apply an arithmetic operation, double-check to ensure no mistake slips in.

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