Sure! Let's solve the equation step-by-step:
We are given the equation:
[tex]\[
\frac{3}{5}(x - 10) = 18 - 4x - 1
\][/tex]
### Step 1: Apply the Distributive Property
To begin, we need to distribute the number outside the parentheses across the terms inside the parentheses on the left side of the equation.
The number that we will distribute is [tex]\(\frac{3}{5}\)[/tex].
Distribute [tex]\(\frac{3}{5}\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(-10\)[/tex]:
[tex]\[
\frac{3}{5} \cdot x - \frac{3}{5} \cdot 10 = \frac{3}{5}x - 6
\][/tex]
So, the equation now becomes:
[tex]\[
\frac{3}{5}x - 6 = 18 - 4x - 1
\][/tex]
### Step 2: Simplify the Right Side
Next, simplify the right side of the equation by combining like terms:
Combine the constants [tex]\(18\)[/tex] and [tex]\(-1\)[/tex]:
[tex]\[
18 - 1 = 17
\][/tex]
So, the simplified equation is:
[tex]\[
\frac{3}{5}x - 6 = 17 - 4x
\][/tex]
### Step 3: Solve for [tex]\(x\)[/tex]
Now, let's get all the [tex]\(x\)[/tex]-terms on one side and constants on the other side. We'll start by adding [tex]\(4x\)[/tex] to both sides to eliminate [tex]\(x\)[/tex] terms on the right side:
[tex]\[
\frac{3}{5}x + 4x - 6 = 17
\][/tex]
Express [tex]\(4x\)[/tex] with a common denominator of [tex]\(5\)[/tex]:
[tex]\[
\frac{3}{5}x + \frac{20}{5}x - 6 = 17
\][/tex]
Combine like terms on the left side:
[tex]\[
\frac{23}{5}x - 6 = 17
\][/tex]
Next, add [tex]\(6\)[/tex] to both sides to isolate the [tex]\(x\)[/tex]-term:
[tex]\[
\frac{23}{5}x = 23
\][/tex]
Finally, solve for [tex]\(x\)[/tex] by multiplying both sides by the reciprocal of [tex]\(\frac{23}{5}\)[/tex]:
[tex]\[
x = 23 \cdot \frac{5}{23}
\][/tex]
[tex]\[
x = 5
\][/tex]
So the solution to the equation is:
[tex]\[
x = 5
\][/tex]
