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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:
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