Sure, let's solve the equation [tex]\( 3(x - 1) = 10(a - 1) \)[/tex] for [tex]\( x \)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
3(x - 1) = 10(a - 1)
\][/tex]
2. Distribute the constants 3 and 10 to the terms inside the parentheses:
[tex]\[
3x - 3 = 10a - 10
\][/tex]
3. Isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
3x - 3 = 10a - 10
\][/tex]
4. Add 3 to both sides to move the constant term to the right side:
[tex]\[
3x = 10a - 10 + 3
\][/tex]
5. Combine the constant terms on the right side:
[tex]\[
3x = 10a - 7
\][/tex]
6. Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{10a - 7}{3}
\][/tex]
So, the solution for [tex]\( x \)[/tex] in terms of [tex]\( a \)[/tex] is:
[tex]\[
x = \frac{10a}{3} - \frac{7}{3}
\][/tex]
Thus, when solved, [tex]\( x \)[/tex] is expressed as:
[tex]\[
x = \frac{10a}{3} - \frac{7}{3}
\][/tex]
This provides the value of [tex]\( x \)[/tex] in terms of the variable [tex]\( a \)[/tex].
