Solve the linear equation.
0.19xplus0.4​(xminus5​)equals​0.01(9xminus3​)

Let's solve the linear equation:

\[
0.19x + 0.4(x - 5) = 0.01(9x - 3)
\]

### Step 1: Distribute the terms

First, distribute the constants \( 0.4 \) and \( 0.01 \) on both sides of the equation:

\[
0.19x + 0.4x - 0.4(5) = 0.01(9x) - 0.01(3)
\]

\[
0.19x + 0.4x - 2 = 0.09x - 0.03
\]

### Step 2: Combine like terms

Now, combine the \( x \)-terms on the left side:

\[
(0.19 + 0.4)x - 2 = 0.09x - 0.03
\]

\[
0.59x - 2 = 0.09x - 0.03
\]

### Step 3: Move \( x \)-terms to one side and constant terms to the other side

Subtract \( 0.09x \) from both sides:

\[
0.59x - 0.09x - 2 = -0.03
\]

\[
0.50x - 2 = -0.03
\]

Now, add 2 to both sides:

\[
0.50x = -0.03 + 2
\]

\[
0.50x = 1.97
\]

### Step 4: Solve for \( x \)

Divide both sides by \( 0.50 \):

\[
x = \frac{1.97}{0.50}
\]

\[
x = 3.94
\]

So, the solution is:

\[
x = 3.94
\]

Would you like further details or explanations?

Here are 5 related questions:
1. How do you solve a system of linear equations?
2. What is the difference between solving linear and quadratic equations?
3. How can you graph the solution of a linear equation?
4. What is the general form of a linear equation?
5. How does distributing terms work in solving equations?

**Tip:** Always double-check your distribution steps to avoid mistakes when solving equations.

Solve the linear equation. 0.19x plus 0.4(x minus 5) equals 0.01(9x minus 3)

Discover how to solve the linear equation 0.19x + 0.4(x - 5) = 0.01(9x - 3) with this detailed, step-by-step solution. Learn about the distributive property, combining like terms, and solving for x. This problem is ideal for students in Grades 8-10.

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