## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

a. $2x+4\lt 5$ b. $2x-4\lt -3$ c. $6x+3\lt 6$ d. $-4x-2\gt -4$
Since $2x+1\lt 2$, then; (a) Adding $3$ to each side of the given inequality; $$3+2x+1\lt 2+3\Longrightarrow2x+4\lt 5$$ (b) Subtracting $5$ from each side of the given inequality; $$2x+1-5\lt 2-5\Longrightarrow 2x-4\lt -3$$ (c) Multiplying each side of the given inequality by $3$; $$3\times(2x+1)\lt 2\times3\Longrightarrow 6x+3\lt 6$$ (d) Multiplying each side of the given inequality by -$2$; $$-2\times(2x+1)\gt 2\times(-2)\Longrightarrow -4x-2\gt -4\\ \text{(The inequality symbol will change since a negative number was multiplied to both sides.)}$$