Solve the following equation for $$ x $$ : $$ 3.45=0.1 x+2.25 $$

Question

UpStudy AI · Accepted Answer

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:**  
$$ x = 12 $$
$$ x = 12 $$

Solve the following equation for \( x \) : \( 3.45=0.1 x+2.25 \)