## Introductory Algebra for College Students (7th Edition)

This inequality is false for every value of $x$; therefore, the inequality has no solution, or $∅$.
To solve the inequality, we need to isolate variables on one side of the inequality and the constants on the other side. First, let's use distributive property: $$3x + 1 \leq 3(x) - 3(2)$$ Multiply: $$3x + 1 \leq 3x - 6$$ Subtract $3x$ from both sides of the inequality: $$(3x - 3x) + 1 \leq (3x - 3x) - 6$$ The $3x$ terms cancel out on both sides of the inequality: $$1 \leq -6$$ This inequality is false for every value of $x$; therefore, the inequality has no solution, or $∅$.