Question: User: Name: ____________ Grade 8 Math Homework Absolute Value Equations Solve each equation. Show all steps and check your solutions. 1. |x| = 9 2. |x - 5| = 7 3. -4 |2x + 3| = -12 4. 3|x - 2| - 4 = 14 5. |4x - 8| = 0 6. -3|x + 6| = 9 Graph shape: a worksheet page with a 2-column by 3-row grid of problem boxes and thin dividing lines, position_hint=top-leftName: Grade 8 Math Homework Compound Inequalities Solve each compound inequality. Graph the solution. 7. -5 < 2x + 3 60; 11 8. -15 < -3x + 6 60; 15 9. 4x - 1 < -9 or 2x + 5 60; 13 10. -2x + 3 > 11 or 3x - 2 60; 10 Graph shapes and math: Top-left: problem 7 asks to graph the compound inequality -5 < 2x + 3 60; 11. Top-right: problem 8 asks to graph the compound inequality -15 < -3x + 6 60; 15. Bottom-left: problem 9 asks to graph the compound inequality 4x - 1 < -9 or 2x + 5 60; 13. Bottom-right: problem 10 asks to graph the compound inequality -2x + 3 > 11 or 3x - 2 60; 10. solve in the picture do not say it do it in the picture

1. Solve |x| = 9 - The absolute value equation |x| = 9 means x can be 9 or -9. - So, $x = 9$ or $x = -9$. 2. Solve |x - 5| = 7 - Set $x - 5 = 7$ or $x - 5 = -7$. - For $x - 5 = 7$, $x = 12$. - For $x - 5 = -7$, $x = -2$. 3. Solve -4|2x + 3| = -12 - Divide both sides by -4: $$\cancel{-4}|2x + 3| = \cancel{-4}\frac{-12}{-4}$$ $$|2x + 3| = 3$$ - Set $2x + 3 = 3$ or $2x + 3 = -3$. - For $2x + 3 = 3$, $2x = 0$, $x = 0$. - For $2x + 3 = -3$, $2x = -6$, $x = -3$. 4. Solve 3|x - 2| - 4 = 14 - Add 4 to both sides: $$3|x - 2| - 4 + 4 = 14 + 4$$ $$3|x - 2| = 18$$ - Divide both sides by 3: $$\cancel{3}|x - 2| = \cancel{3}6$$ $$|x - 2| = 6$$ - Set $x - 2 = 6$ or $x - 2 = -6$. - For $x - 2 = 6$, $x = 8$. - For $x - 2 = -6$, $x = -4$. 5. Solve |4x - 8| = 0 - Absolute value equals zero only if the inside is zero: $$4x - 8 = 0$$ - Solve for $x$: $$4x = 8$$ $$x = 2$$ 6. Solve -3|x + 6| = 9 - Divide both sides by -3: $$\cancel{-3}|x + 6| = \cancel{-3}\frac{9}{-3}$$ $$|x + 6| = -3$$ - Absolute value cannot be negative, so no solution. Final answers: 1. $x = 9$ or $x = -9$ 2. $x = 12$ or $x = -2$ 3. $x = 0$ or $x = -3$ 4. $x = 8$ or $x = -4$ 5. $x = 2$ 6. No solution