Certainly! Let's solve the inequality [tex]\( x + 2y \leq 12 \)[/tex] step-by-step, assuming we need to find the maximum possible integer value for [tex]\( x \)[/tex] when [tex]\( y \)[/tex] is given.
### Step-by-Step Solution:
1. Consider the given inequality:
[tex]\[
x + 2y \leq 12
\][/tex]
2. Simplify for [tex]\( x \)[/tex]:
To find the maximum value of [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] in the inequality. Subtract [tex]\( 2y \)[/tex] from both sides of the inequality:
[tex]\[
x \leq 12 - 2y
\][/tex]
3. Given value of [tex]\( y \)[/tex]:
Suppose [tex]\( y \)[/tex] is provided as 3.
4. Substitute [tex]\( y \)[/tex] in the inequality:
Replace [tex]\( y \)[/tex] with 3 in the inequality:
[tex]\[
x \leq 12 - 2 \times 3
\][/tex]
5. Calculate the value on the right-hand side:
Perform the multiplication and subtraction:
[tex]\[
x \leq 12 - 6
\][/tex]
[tex]\[
x \leq 6
\][/tex]
6. Determine the maximum integer value for [tex]\( x \)[/tex]:
The maximum possible integer value for [tex]\( x \)[/tex] that satisfies the inequality [tex]\( x \leq 6 \)[/tex] is indeed 6.
So, the maximum possible integer value for [tex]\( x \)[/tex], given [tex]\( y = 3 \)[/tex], is [tex]\( x = 6 \)[/tex].
