To determine the value of [tex]\( w \)[/tex] that satisfies the equation
[tex]\[
\frac{5w + 4}{3} = \frac{3w}{2},
\][/tex]
we will solve the equation step by step.
1. Clear the denominators by finding a common multiple:
The common multiple of 3 and 2 is 6. Multiply both sides of the equation by 6 to eliminate the fractions:
[tex]\[
6 \cdot \frac{5w + 4}{3} = 6 \cdot \frac{3w}{2}.
\][/tex]
2. Simplify both sides:
[tex]\[
6 \cdot \frac{5w + 4}{3} = 2 \cdot (5w + 4) = 10w + 8,
\][/tex]
and
[tex]\[
6 \cdot \frac{3w}{2} = 3 \cdot (3w) = 9w.
\][/tex]
So, the equation becomes:
[tex]\[
10w + 8 = 9w.
\][/tex]
3. Isolate the variable [tex]\( w \)[/tex]:
Subtract [tex]\( 9w \)[/tex] from both sides to isolate [tex]\( w \)[/tex] on one side of the equation:
[tex]\[
10w + 8 - 9w = 9w - 9w,
\][/tex]
which simplifies to:
[tex]\[
w + 8 = 0.
\][/tex]
4. Solve for [tex]\( w \)[/tex]:
Subtract 8 from both sides:
[tex]\[
w = -8.
\][/tex]
Hence, the value of [tex]\( w \)[/tex] that makes the equation true is [tex]\(-8\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-8}
\][/tex]
