To solve the given equation [tex]\(\frac{2}{3} x - \frac{2}{4} = \frac{6}{4}\)[/tex] for [tex]\(x = 3\)[/tex], we can follow these steps:
1. Substitute the given value of [tex]\(x\)[/tex] into the equation:
[tex]\[
\frac{2}{3} \cdot 3 - \frac{2}{4} = \frac{6}{4}
\][/tex]
2. Compute the first term [tex]\(\frac{2}{3} \cdot 3\)[/tex]:
[tex]\[
\frac{2}{3} \cdot 3 = 2
\][/tex]
3. Compute the second term [tex]\(\frac{2}{4}\)[/tex]:
[tex]\[
\frac{2}{4} = \frac{1}{2} = 0.5
\][/tex]
4. Compute the right-hand side of the equation:
[tex]\[
\frac{6}{4} = \frac{3}{2} = 1.5
\][/tex]
5. Substitute the computed values from the left-hand side and verify against the right-hand side:
[tex]\[
2 - 0.5 = 1.5
\][/tex]
6. Conclusion:
After computing and substituting back with [tex]\(x = 3\)[/tex], the left-hand side simplifies to [tex]\(1.5\)[/tex], which matches the right-hand side [tex]\(\frac{6}{4}\)[/tex]. This confirms our solution is consistent and accurate.
So, the detailed step-by-step results are:
- [tex]\((2.0, 0.5, 1.5, 1.5)\)[/tex]
Thus, the solution verifies the correctness of the original equation with [tex]\(x = 3\)[/tex].
