Certainly! Let's solve the equation [tex]\(\frac{x-1}{2} = \frac{x+2}{5}\)[/tex] step by step.
1. Start with the given equation:
[tex]\[
\frac{x-1}{2} = \frac{x+2}{5}
\][/tex]
2. Eliminate the fractions by finding a common denominator, which is 10 in this case. Multiply both sides of the equation by 10:
[tex]\[
10 \cdot \frac{x-1}{2} = 10 \cdot \frac{x+2}{5}
\][/tex]
3. Simplify both sides:
[tex]\[
5(x - 1) = 2(x + 2)
\][/tex]
4. Distribute the constants on both sides of the equation:
[tex]\[
5x - 5 = 2x + 4
\][/tex]
5. Move all terms involving [tex]\(x\)[/tex] to one side of the equation and constants to the other side. Subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[
5x - 2x - 5 = 4
\][/tex]
6. Combine like terms:
[tex]\[
3x - 5 = 4
\][/tex]
7. Add 5 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
3x - 5 + 5 = 4 + 5
\][/tex]
[tex]\[
3x = 9
\][/tex]
8. Finally, divide by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{9}{3}
\][/tex]
[tex]\[
x = 3
\][/tex]
Therefore, the solution is [tex]\(\boxed{3}\)[/tex].
