Question

solve and check the following equation. 0.14y + 0.09(y + 8000) = 2560 the solution set is {□}.

Explanation:

Step1: Expand the parentheses

$0.14y + 0.09y + 0.09\times8000 = 2560$
$0.14y + 0.09y + 720 = 2560$

Step2: Combine like terms

$0.23y + 720 = 2560$

Step3: Isolate the variable term

$0.23y = 2560 - 720$
$0.23y = 1840$

Step4: Solve for y

$y = \frac{1840}{0.23}$
$y = 8000$

Step5: Check the solution

Substitute $y=8000$ into original equation:
$0.14\times8000 + 0.09(8000+8000) = 1120 + 0.09\times16000 = 1120 + 1440 = 2560$
The left-hand side equals the right-hand side, so the solution is valid.

Answer:

$\{8000\}$