Answer :
Certainly! Let's solve the inequality step by step:
We want to solve the inequality:
[tex]\[ -6x + 11 \leq -9x + 2 \][/tex]
Step 1: Move the terms involving [tex]\( x \)[/tex] to one side of the inequality.
To do this, we'll add [tex]\( 9x \)[/tex] to both sides:
[tex]\[ -6x + 9x + 11 \leq 2 \][/tex]
Step 2: Combine the like terms.
On the left side, combine [tex]\( -6x + 9x \)[/tex]:
[tex]\[ 3x + 11 \leq 2 \][/tex]
Step 3: Isolate the term with [tex]\( x \)[/tex] by moving the constant on the left side to the right side.
Subtract 11 from both sides:
[tex]\[ 3x \leq 2 - 11 \][/tex]
Step 4: Simplify the right side.
Calculate [tex]\( 2 - 11 \)[/tex]:
[tex]\[ 3x \leq -9 \][/tex]
Step 5: Solve for [tex]\( x \)[/tex] by dividing both sides by 3.
Divide both sides of the inequality by 3:
[tex]\[ x \leq \frac{-9}{3} \][/tex]
Simplifying the division gives:
[tex]\[ x \leq -3 \][/tex]
Therefore, the solution to the inequality is [tex]\( x \leq -3 \)[/tex].
The correct answer is:
[tex]\[ \text{A. } x \leq -3 \][/tex]
We want to solve the inequality:
[tex]\[ -6x + 11 \leq -9x + 2 \][/tex]
Step 1: Move the terms involving [tex]\( x \)[/tex] to one side of the inequality.
To do this, we'll add [tex]\( 9x \)[/tex] to both sides:
[tex]\[ -6x + 9x + 11 \leq 2 \][/tex]
Step 2: Combine the like terms.
On the left side, combine [tex]\( -6x + 9x \)[/tex]:
[tex]\[ 3x + 11 \leq 2 \][/tex]
Step 3: Isolate the term with [tex]\( x \)[/tex] by moving the constant on the left side to the right side.
Subtract 11 from both sides:
[tex]\[ 3x \leq 2 - 11 \][/tex]
Step 4: Simplify the right side.
Calculate [tex]\( 2 - 11 \)[/tex]:
[tex]\[ 3x \leq -9 \][/tex]
Step 5: Solve for [tex]\( x \)[/tex] by dividing both sides by 3.
Divide both sides of the inequality by 3:
[tex]\[ x \leq \frac{-9}{3} \][/tex]
Simplifying the division gives:
[tex]\[ x \leq -3 \][/tex]
Therefore, the solution to the inequality is [tex]\( x \leq -3 \)[/tex].
The correct answer is:
[tex]\[ \text{A. } x \leq -3 \][/tex]
