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Chapter 5: Problem 27

Solve the equations. $$8.4 x+6=48$$

Short Answer

Expert verified
x = 5

Step by step solution

01

- Subtract 6 from both sides

To isolate the variable term, subtract 6 from both sides of the equation: =-42$$
02

- Divide by 8.4

Next, divide both sides of the equation by 8.4 to solve for x: =

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Key Concepts

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

isolating the variable
In solving linear equations, the first step is often 'isolating the variable.' This means getting the variable (like x) by itself on one side of the equation. To do this, we need to remove any numbers that are added, subtracted, multiplied, or divided by the variable. The goal is to have an equation that looks like 'x = (something).' Isolating the variable simplifies the equation, making it easier to solve.
subtracting terms
One common method to isolate the variable is 'subtracting terms.' In the given problem, the equation is: 8.4x + 6 = 48.
Here, we need to get rid of the +6 to isolate the term with x. To do this, subtract 6 from both sides of the equation:
\(8.4x + 6 - 6 = 48 - 6\)
This simplifies to:
\(8.4x = 42\)
Subtracting terms helps move numbers from one side of the equation to the other, maintaining balance.
dividing terms
After subtracting terms, the next often step is 'dividing terms' to completely isolate the variable. From the previous step, our equation is now:
\[8.4x = 42\]
Here, 8.4x means 8.4 multiplied by x. To separate x, we divide both sides by 8.4:
\(\frac{8.4x}{8.4} = \frac{42}{8.4}\)\
This simplifies to: \(x = 5\)
By dividing terms, we ensure that we only have the variable left on one side, giving us the answer directly.
prealgebra
The process demonstrated falls under 'prealgebra'. Prealgebra involves basic algebraic operations and prepares students for more advanced algebra. It includes:
  • Understanding variables
  • Performing arithmetic operations with variables
  • Solving simple linear equations
    In this problem, we used prealgebra techniques like subtraction and division to solve the equation: \(8.4x + 6 = 48\).
    Mastering prealgebra is essential as it forms the foundation for solving more complex algebraic equations in later studies.

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