1. Solve the equation $10x + 3 = 32$ for $x$. Subtract 3 from both sides to isolate the term with $x$: $$10x + 3 - 3 = 32 - 3$$ $$10x = 29$$ Divide both sides by 10 to solve for $x$: $$x = \frac{29}{10} = 2.9$$ 2. Interpret the expression $\log_a 29$ where $a$ is the base of the logarithm. This expression means the power to which you raise $a$ to get 29. Without more info, no simplification is possible. 3. Justify each statement using the property letter: 5. If $10x + y = 32$ and $y = 3$, then substituting gives $10x + 3 = 32$, which simplifies to $4x + 3 = 7$ (assuming a step missing contextually). The step from $y = 3$ to substitution uses the **Substitution Property (F)**. 6. $\angle A = \angle A$ states equality of an angle to itself: **Reflexive Property (G)**. 7. If $p = -2$, then multiply both sides by 2: $2p = 2\times(-2) = -4$ uses **Multiplication Property of Equality (C)**. 8. If $6m = 54$, divide both sides by 6 to solve for $m$: $m = \frac{54}{6} = 9$ uses **Division Property of Equality (D)**. 9. If $3r = s$, then by the symmetric property, $s = 3r$ uses **Symmetric Property (H)**. 10. If $(2/3)h = 14$, subtract 5 from both sides: $(2/3)h - 5 = 14 - 5$ uses **Subtraction Property of Equality (B)**. 11. Given $KL - RL = KR$, add $RL$ to both sides: $KL = KR + RL$ uses **Addition Property of Equality (A)**. 12. Distribute $t$ over $(q + r)$: $t(q + r) = tq + tr$ uses the **Distributive Property (E)**. 13. Given $\angle A + \angle B = \angle C$ and $\angle C = 2\angle D$, then by substitution: $$\angle A + \angle B = 2\angle D$$ uses **Substitution Property (F)**. Summary of answers: 5: F 6: G 7: C 8: D 9: H 10: B 11: A 12: E 13: F Final answer for problem 1: $$x = 2.9$$