Question

solve the equation
2 = 9 + |8t + 3|
the solution set is .

Explanation:

Step1: Isolate the absolute value

Subtract 9 from both sides of the equation \(2 = 9+\vert8t + 3\vert\).
\(2-9=\vert8t + 3\vert\)
\(-7=\vert8t + 3\vert\)

Step2: Analyze the absolute value equation

The absolute value of a number is always non - negative (i.e., \(\vert x\vert\geq0\) for all real numbers \(x\)). Here, we have \(\vert8t + 3\vert=-7\), but the absolute value of an expression cannot be negative.

Answer:

\(\varnothing\) (the empty set)