Question
Solve the following equation for \( x \) : \( 3.45=0.1 x+2.25 \)
Ask by Tyler Lane. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 12 \)
Solution
To solve the equation \( 3.45 = 0.1x + 2.25 \) for \( x \), follow these steps:
1. **Subtract 2.25 from both sides:**
This isolates the term containing \( x \) on one side of the equation.
\[
3.45 - 2.25 = 0.1x + 2.25 - 2.25
\]
\[
1.20 = 0.1x
\]
2. **Divide both sides by 0.1:**
This step solves for \( x \) by getting rid of the coefficient (0.1) multiplying \( x \).
\[
\frac{1.20}{0.1} = \frac{0.1x}{0.1}
\]
\[
12 = x
\]
3. **Write the solution:**
\[
x = 12
\]
**Verification (Optional):**
To ensure that the solution is correct, substitute \( x = 12 \) back into the original equation:
\[
3.45 = 0.1(12) + 2.25
\]
\[
3.45 = 1.2 + 2.25
\]
\[
3.45 = 3.45
\]
Since both sides of the equation are equal, the solution \( x = 12 \) is correct.
**Final Answer:**
\( x = 12 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve the equation \( 3.45 = 0.1x + 2.25 \), we start by isolating the term involving \( x \). First, subtract \( 2.25 \) from both sides: \[ 3.45 - 2.25 = 0.1x \] This simplifies to: \[ 1.20 = 0.1x \] Next, divide both sides by \( 0.1 \): \[ x = \frac{1.20}{0.1} \] This leads to: \[ x = 12 \] So, the solution to the equation is \( x = 12 \).
