Subjects algebra

Linear Equations 6798E5

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1. **Problem 2:** Solve the equation $$\frac{x - 10}{4} = -5 = 20$$. This looks like a formatting issue. Assuming the problem is $$\frac{x - 10}{4} = -5$$ (since the extra = 20 is likely a typo). Use the formula for solving linear equations: multiply both sides by the denominator to isolate $x$. $$\frac{x - 10}{4} = -5$$ Multiply both sides by 4: $$\cancel{4} \times \frac{x - 10}{\cancel{4}} = -5 \times 4$$ $$x - 10 = -20$$ Add 10 to both sides: $$x - 10 + 10 = -20 + 10$$ $$x = -10$$ 2. **Problem 3:** Solve the equation $$\frac{x + 8}{3} = 4$$. Multiply both sides by 3: $$\cancel{3} \times \frac{x + 8}{\cancel{3}} = 4 \times 3$$ $$x + 8 = 12$$ Subtract 8 from both sides: $$x + 8 - 8 = 12 - 8$$ $$x = 4$$ 3. **Problem 4:** Solve the equation $$-8x + 3 = -13 - 3$$. Simplify the right side: $$-8x + 3 = -16$$ Subtract 3 from both sides: $$-8x + 3 - 3 = -16 - 3$$ $$-8x = -19$$ Divide both sides by -8: $$\frac{-8x}{\cancel{-8}} = \frac{-19}{-8}$$ $$x = \frac{19}{8}$$ **Final answers:** 2) $x = -10$ 3) $x = 4$ 4) $x = \frac{19}{8}$