To determine which value of [tex]\( x \)[/tex] could not satisfy the given constraints, let's proceed step by step.
Step 1: Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]
Starting with the equation [tex]\( 4x + 2y = 20 \)[/tex], we can isolate [tex]\( y \)[/tex]:
[tex]\[ 2y = 20 - 4x \][/tex]
[tex]\[ y = 10 - 2x \][/tex]
Step 2: Apply the constraint [tex]\( y \geq 4 \)[/tex]
We need to find out which values of [tex]\( x \)[/tex] make [tex]\( y \geq 4 \)[/tex]:
[tex]\[ 10 - 2x \geq 4 \][/tex]
[tex]\[ 10 - 4 \geq 2x \][/tex]
[tex]\[ 6 \geq 2x \][/tex]
[tex]\[ 3 \geq x \][/tex]
This simplifies to:
[tex]\[ x \leq 3 \][/tex]
Step 3: Test each option to see if it satisfies [tex]\( x \leq 3 \)[/tex]
- Option A: [tex]\( x = -6 \)[/tex]
[tex]\[ -6 \leq 3 \][/tex] is true, thus [tex]\( x = -6 \)[/tex] is feasible.
- Option B: [tex]\( x = -3 \)[/tex]
[tex]\[ -3 \leq 3 \][/tex] is true, thus [tex]\( x = -3 \)[/tex] is feasible.
- Option C: [tex]\( x = 3 \)[/tex]
[tex]\[ 3 \leq 3 \][/tex] is true, thus [tex]\( x = 3 \)[/tex] is feasible.
- Option D: [tex]\( x = 6 \)[/tex]
[tex]\[ 6 \leq 3 \][/tex] is false, thus [tex]\( x = 6 \)[/tex] is not feasible.
Conclusion
Given the constraints of the equation [tex]\( 4x + 2y = 20 \)[/tex] and [tex]\( y \geq 4 \)[/tex], the value of [tex]\( x \)[/tex] that could not be is [tex]\( \boxed{6} \)[/tex].
