Answer :
Sure! Let's solve the inequality step-by-step.
We start with the inequality:
[tex]\[ 54 - 10x \leq 20 + 7x \][/tex]
1. Move all terms involving [tex]\( x \)[/tex] to one side by subtracting [tex]\( 7x \)[/tex] from both sides:
[tex]\[ 54 - 10x - 7x \leq 20 \][/tex]
2. Combine the like terms on the left side:
[tex]\[ 54 - 17x \leq 20 \][/tex]
3. Move the constant term on the left side to the right side by subtracting [tex]\( 54 \)[/tex] from both sides:
[tex]\[ -17x \leq 20 - 54 \][/tex]
4. Simplify the constants on the right side:
[tex]\[ -17x \leq -34 \][/tex]
5. Divide both sides of the inequality by [tex]\(-17\)[/tex] (since we are dividing by a negative number, we must reverse the inequality sign):
[tex]\[ x \geq \frac{-34}{-17} \][/tex]
6. Simplify the fraction:
[tex]\[ x \geq 2 \][/tex]
So the correct answer is [tex]\( x \geq 2 \)[/tex], which corresponds to option:
B. [tex]\( x \geq 2 \)[/tex]
We start with the inequality:
[tex]\[ 54 - 10x \leq 20 + 7x \][/tex]
1. Move all terms involving [tex]\( x \)[/tex] to one side by subtracting [tex]\( 7x \)[/tex] from both sides:
[tex]\[ 54 - 10x - 7x \leq 20 \][/tex]
2. Combine the like terms on the left side:
[tex]\[ 54 - 17x \leq 20 \][/tex]
3. Move the constant term on the left side to the right side by subtracting [tex]\( 54 \)[/tex] from both sides:
[tex]\[ -17x \leq 20 - 54 \][/tex]
4. Simplify the constants on the right side:
[tex]\[ -17x \leq -34 \][/tex]
5. Divide both sides of the inequality by [tex]\(-17\)[/tex] (since we are dividing by a negative number, we must reverse the inequality sign):
[tex]\[ x \geq \frac{-34}{-17} \][/tex]
6. Simplify the fraction:
[tex]\[ x \geq 2 \][/tex]
So the correct answer is [tex]\( x \geq 2 \)[/tex], which corresponds to option:
B. [tex]\( x \geq 2 \)[/tex]
