Question

solve and check the following linear equation.
26 - 2 + 9y - 4(y + 3) = -5(3y - 5) - 6(y - 1) - 14y + 13
what is the solution? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}.
b. the solution set is {x | x is a real number}.
c. the solution set is ∅.

Explanation:

Step1: Expand inner parentheses

Left side: $26 - [2 + 9y - 4y - 12]$
Right side: $-5(3y - 5) - [6y - 6 - 14y + 13]$

Step2: Simplify brackets

Left side: $26 - [5y - 10]$
Right side: $-15y + 25 - [-8y + 7]$

Step3: Remove outer brackets

Left side: $26 - 5y + 10$
Right side: $-15y + 25 + 8y - 7$

Step4: Combine like terms

Left side: $36 - 5y$
Right side: $-7y + 18$

Step5: Isolate y terms

$36 - 5y + 7y = 18$

Step6: Combine y terms

$36 + 2y = 18$

Step7: Isolate constant terms

$2y = 18 - 36$

Step8: Calculate right-hand side

$2y = -18$

Step9: Solve for y

$y = \frac{-18}{2} = -9$

Step10: Verify solution

Substitute $y=-9$ into original equation:
Left: $26 - [2 + 9(-9) - 4(-9+3)] = 26 - [2 -81 +24] = 26 - (-55) = 81$
Right: $-5(3(-9)-5) - [6(-9-1)-14(-9)+13] = -5(-32) - [-60+126+13] = 160 - 79 = 81$
Both sides are equal, so $y=-9$ is valid.

Answer:

A. The solution set is $\{-9\}$