Sure, let's solve the inequality step-by-step.
Given the inequality:
[tex]\[ 11 - 6x \leq 5 - 8x \][/tex]
Step 1: Eliminate the [tex]\( -8x \)[/tex] term on the right side by adding [tex]\( 8x \)[/tex] to both sides:
[tex]\[ 11 - 6x + 8x \leq 5 - 8x + 8x \][/tex]
This simplifies to:
[tex]\[ 11 + 2x \leq 5 \][/tex]
Step 2: Isolate the term with [tex]\( x \)[/tex] on the left side by subtracting 11 from both sides:
[tex]\[ 11 + 2x - 11 \leq 5 - 11 \][/tex]
This simplifies to:
[tex]\[ 2x \leq -6 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ \frac{2x}{2} \leq \frac{-6}{2} \][/tex]
This simplifies to:
[tex]\[ x \leq -3 \][/tex]
So the solution to the inequality is:
[tex]\[ x \leq -3 \][/tex]
In interval notation, the solution is:
[tex]\[ (-\infty, -3] \][/tex]
