Solve the inequality 5x + 15/4 - 2x > 0.

Step-by-step solution

1. 1

   Combine the like terms on the left. The two $x$ terms sit on the same side, so add their coefficients before anything else:

   $5x-2x=3x\quad\Longrightarrow\quad 3x+\frac{15}{4}>0$

2. 2

   Isolate the variable term. Subtract $\tfrac{15}{4}$ from both sides:

   $3x>-\frac{15}{4}$

3. 3

   Divide by $3$, keeping the fraction exact. Dividing by a positive number does not change the direction:

   $x>-\frac{15}{4}\cdot\frac{1}{3}=-\frac{15}{12}=-\frac{5}{4}$

   Reduce $\tfrac{15}{12}$ by the common factor $3$ rather than converting to $-1.25$ — the exact fraction is the preferred form of the answer.

4. 4

   Verify the boundary and one interior point. At $x=-\tfrac54$: $3\left(-\tfrac54\right)+\tfrac{15}{4}=-\tfrac{15}{4}+\tfrac{15}{4}=0$, which is not $>0$, so the endpoint is correctly excluded. At $x=0$: $\tfrac{15}{4}>0$ $\checkmark$. At $x=-2$: $-6+3.75=-2.25\not>0$ $\checkmark$.