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Chapter 8: Problem 57

Solve. $$ 0.05+x=2.525 $$

Short Answer

Expert verified
x = 2.475

Step by step solution

01

Identify the equation to solve

The given equation is: 0.05 + x = 2.525
02

Isolate the variable

To solve for x, isolate it by subtracting 0.05 from both sides of the equation: 0.05 + x - 0.05 = 2.525 - 0.05
03

Simplify both sides of the equation

By subtracting 0.05 from both sides, we get: x = 2.475
04

Verify the solution

Substitute x back into the original equation to check the solution: 0.05 + 2.475 Simplifying this, we get 2.525, which matches the original equation, confirming that x = 2.475 is correct.

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Key Concepts

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

Isolate the Variable
Isolating the variable is a critical step in solving linear equations. This means getting the variable (in this case, x) alone on one side of the equation, so we can directly find its value. In our example, the equation is: 0.05 + x = 2.525.
To isolate x, you need to perform the same mathematical operation on both sides of the equation. Here, we subtract 0.05 from both sides:
\[ 0.05 + x - 0.05 = 2.525 - 0.05 \] This leaves us with: \[ x = 2.475 \]By isolating the variable, you make it simpler to solve for x. Always ensure that the operation is applied uniformly to maintain the equality of the equation.
Verification of Solution
After isolating the variable and finding its value, the next important step is to verify the solution. This ensures that the solution is correct and satisfies the original equation. To verify the solution, substitute the value of x back into the original equation: \[0.05 + x = 2.525 \]Replace x with the solved value:\[0.05 + 2.475 \]Simplify this: \[0.05 + 2.475 = 2.525 \]Since both sides of the equation are equal, the solution is verified. Verification helps prevent mistakes and gives confidence that the obtained solution is indeed correct.
Simplifying Equations
Simplifying equations involves making the equation as straightforward as possible. This is done by performing operations that combine like terms, or in our case, removing constants by subtraction. When faced with an equation like:\[0.05 + x = 2.525\] We simplify it by subtracting 0.05 from both sides. This gives:\[x = 2.475\]Simplification may include addition, subtraction, multiplication, or division applied uniformly to both sides. The goal of simplification is to make the equation easier to solve and interpret. Remember, the key is to keep the equation balanced by performing equivalent operations on both sides.

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Most popular questions from this chapter

A physician orders \(40 \mathrm{~mL}\) of \(5 \%\) dextrose in water (D5W) solution to be administered intravenously over \(2 \mathrm{hr}\) to an elderly patient. How many liters of D5W is this?

Convert to Celsius. Use the formula \(C=\frac{5}{9} \cdot(F-32)\) or \(C=\frac{F-32}{1.8}\). $$ 140^{\circ} \mathrm{F} $$

\(806 \mathrm{~L}=\) __________ \(\mathrm{mL}\)

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