Zero Solutions 703Db0

1. **State the problem:** We are given the equation $$-\frac{3}{2}x - 2 = hx + 4$$ and asked to find the value of $h$ for which the equation has zero solutions. 2. **Recall the rule for zero solutions:** An equation has zero solutions when the variable terms on both sides are equal (same coefficient) but the constants are different, resulting in a contradiction. 3. **Set the coefficients of $x$ equal:** For zero solutions, the coefficient of $x$ on the left must equal the coefficient on the right: $$-\frac{3}{2} = h$$ 4. **Check the constants:** The constants on each side are $-2$ on the left and $4$ on the right. Since these are not equal, the equation will have zero solutions. 5. **Complete the sentence:** - $h = -\frac{3}{2}$ - You get zero solutions when you have **the same** number of $x$'s on either side of the equation - and **different constants**. **Final answer:** This equation will have zero solutions when $h = -\frac{3}{2}$ because you get zero solutions when you have the same number of $x$'s on either side of the equation and different constants.