Sure, let's solve the given equation step-by-step.
The given equation is:
[tex]\[
\left(-\frac{3}{7} x + \frac{18}{3s}\right) = 1 - 6x
\][/tex]
First, let's isolate the variable [tex]\( x \)[/tex].
Step 1: Expand and combine like terms.
- To remove fractions, it's sometimes helpful to multiply through by the least common denominator. In this case, we'll work step-by-step through simple operations to maintain clarity.
- Multiply the terms involving [tex]\( x \)[/tex]:
[tex]\[
-\frac{3}{7} x + \frac{18}{3s} = 1 - 6x
\][/tex]
Step 2: Get all terms involving [tex]\( x \)[/tex] on one side of the equation and constants on the other.
Add [tex]\( 6x \)[/tex] to both sides:
[tex]\[
-\frac{3}{7} x + 6x + \frac{18}{3s} = 1
\][/tex]
Step 3: Combine terms involving [tex]\( x \)[/tex]:
[tex]\[
\left(-\frac{3}{7} + 6\right)x + \frac{18}{3s} = 1
\][/tex]
Simplify the coefficients of [tex]\( x \)[/tex]:
[tex]\[
\left(6 - \frac{3}{7}\right)x + \frac{18}{3s} = 1
\][/tex]
Convert [tex]\(6\)[/tex] to a fraction with a denominator of [tex]\(7\)[/tex]:
[tex]\[
\left(\frac{42}{7} - \frac{3}{7}\right)x + \frac{18}{3s} = 1
\][/tex]
Combine the fractions:
[tex]\[
\frac{39}{7}x + \frac{18}{3s} = 1
\][/tex]
Step 4: Isolate [tex]\( x \)[/tex]:
Subtract [tex]\(\frac{18}{3s}\)[/tex] from both sides:
[tex]\[
\frac{39}{7}x = 1 - \frac{18}{3s}
\][/tex]
Step 5: Solve for [tex]\( x \)[/tex]:
Multiply both sides by [tex]\(\frac{7}{39}\)[/tex]:
[tex]\[
x = \frac{7}{39} \left(1 - \frac{18}{3s}\right)
\][/tex]
Simplify the right side:
[tex]\[
x = \frac{7}{39} \left(\frac{3s - 18}{3s}\right)
\][/tex]
Step 6: Distribute [tex]\(\frac{7}{39}\)[/tex] across the fraction:
Simplify the fraction inside:
[tex]\[
x = \frac{7}{39} \cdot \frac{3(s - 6)}{3s}
\][/tex]
This simplifies to:
[tex]\[
x = \frac{7}{39} \cdot \frac{s - 6}{s}
\][/tex]
Combine the constants:
[tex]\[
x = \frac{7}{39} \cdot \frac{s - 6}{s} = \frac{7(s - 6)}{39s}
\][/tex]
Finally, simplify further:
[tex]\[
x = \frac{7}{39s} (s - 6)
\][/tex]
Combining the fractions gives us:
[tex]\[
x = \frac{7(s - 6)}{39s} = \frac{1}{5.57} \cdot \frac{s - 6}{s}
\][/tex]
So, [tex]\( x \)[/tex] can be computed as:
[tex]\[
x = 0.179487179487179 \cdot \frac{s - 6}{s}
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
x = 0.179487179487179 \cdot \frac{s - 6}{s}
\][/tex]
This provides a detailed step-by-step solution to the given equation.
