3. Answer: x > -5
Step-by-step explanation:
[tex]\dfrac{9x+1}{4}>2x-1\\\\\\\dfrac{9x+1}{4}(4)>4(2x-1)\\\\\\9x+1>8x-4\\\\x+1>-4\quad \rightarrow \text{subtracted 8x from both sides}\\\\x>-5\quad \rightarrow \text{subtracted 1 from both sides}\\[/tex]
4. Answer: [tex]\bold{y\leq \dfrac{28}{5}}[/tex]
Step-by-step explanation:
[tex]8y-3y+1\leq 29\\\\.\qquad 5y + 1 \leq 29\\\\.\qquad 5y\quad \leq 28\\\\.\qquad y\quad \leq \dfrac{28}{5}\\[/tex]
7. Answer: x > -24
Step-by-step explanation:
[tex]\dfrac{x}{3}-1<\dfrac{x}{2}+3\\\\\\\dfrac{x}{3}(6)-1(6)<\dfrac{x}{2}(6)+3(6)\\\\\\2x - 6 < 3x + 18\\\\.\quad -6<x + 18\\\\.\quad -24<x\quad \rightarrow \quad x > -24[/tex]
