Let's solve the given equation step-by-step:
[tex]\[ 9 \times (2x - 1) = 3^4 - 2x \][/tex]
1. Calculate [tex]\(3^4\)[/tex]:
[tex]\[ 3^4 = 81 \][/tex]
So, the equation becomes:
[tex]\[ 9 \times (2x - 1) = 81 - 2x \][/tex]
2. Distribute 9 on the left side:
[tex]\[ 9 \times (2x - 1) = 9 \times 2x - 9 \times 1 \][/tex]
[tex]\[ 18x - 9 = 81 - 2x \][/tex]
3. Combine like terms by adding [tex]\(2x\)[/tex] to both sides:
[tex]\[ 18x - 9 + 2x = 81 - 2x + 2x \][/tex]
[tex]\[ 20x - 9 = 81 \][/tex]
4. Isolate the term with [tex]\(x\)[/tex] by adding 9 to both sides:
[tex]\[ 20x - 9 + 9 = 81 + 9 \][/tex]
[tex]\[ 20x = 90 \][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides by 20:
[tex]\[ x = \frac{90}{20} \][/tex]
[tex]\[ x = 4.5 \][/tex]
Therefore, the solution to the equation is:
[tex]\[ x = 4.5 \][/tex]
