1. **Problem a:** Rearrange $-3y - 6 = -2\sqrt{7}x - 3$ to solve for $x$. Step 1: Add 3 to both sides: $$-3y - 6 + 3 = -2\sqrt{7}x$$ $$-3y - 3 = -2\sqrt{7}x$$ Step 2: Divide both sides by $-2\sqrt{7}$: $$x = \frac{-3y - 3}{-2\sqrt{7}} = \frac{3y + 3}{2\sqrt{7}}$$ 2. **Problem b:** Rearrange $\sqrt{y} + 3 = \sqrt{y} + 8x$ to solve for $x$. Step 1: Subtract $\sqrt{y}$ from both sides: $$3 = 8x$$ Step 2: Divide both sides by 8: $$x = \frac{3}{8}$$ 3. **Problem c:** Rearrange $$\sqrt[3]{\frac{-8(x + y)}{3(x - y)}} = -10$$ to solve for $x$. Step 1: Cube both sides to remove the cube root: $$\frac{-8(x + y)}{3(x - y)} = (-10)^3 = -1000$$ Step 2: Multiply both sides by $3(x - y)$: $$-8(x + y) = -1000 \times 3(x - y)$$ $$-8(x + y) = -3000(x - y)$$ Step 3: Divide both sides by $-1$: $$8(x + y) = 3000(x - y)$$ Step 4: Expand both sides: $$8x + 8y = 3000x - 3000y$$ Step 5: Bring all $x$ terms to one side and $y$ terms to the other: $$8x - 3000x = -3000y - 8y$$ $$-2992x = -3008y$$ Step 6: Divide both sides by $-2992$: $$x = \frac{-3008y}{-2992} = \frac{3008}{2992}y = \frac{188}{187}y$$ **Final answers:** - a) $x = \frac{3y + 3}{2\sqrt{7}}$ - b) $x = \frac{3}{8}$ - c) $x = \frac{188}{187}y$