1. **Problem 14:** Find which algebraic expression is equivalent. Given expressions: A) $32k + 5 - 2k + 1$ B) $6 + 24k - 6k$ 2. **Simplify expression A:** Combine like terms: $$32k - 2k + 5 + 1 = (32k - 2k) + (5 + 1) = 30k + 6$$ 3. **Simplify expression B:** Combine like terms: $$6 + 24k - 6k = 6 + (24k - 6k) = 6 + 18k$$ 4. **Compare simplified expressions:** Expression A is $30k + 6$ Expression B is $18k + 6$ They are not equivalent because the coefficients of $k$ differ. --- 5. **Problem 15:** Find the value of $x$ from the set ${20, 21, 22, 23}$ that satisfies $6x = 132$. 6. **Solve the equation:** $$6x = 132$$ Divide both sides by 6: $$\cancel{6}x = \cancel{6} \times 22$$ $$x = 22$$ 7. **Check if $x=22$ is in the set:** Yes, 22 is in the set ${20, 21, 22, 23}$. 8. **Solve for $x$ in the equation $\frac{x}{6.5} = 3$:** Multiply both sides by 6.5: $$\cancel{\frac{x}{\cancel{6.5}}} \times \cancel{6.5} = 3 \times 6.5$$ $$x = 19.5$$ **Final answers:** - Expression equivalent to A is $30k + 6$. - Value of $x$ from the set that satisfies $6x=132$ is $22$. - Solution to $\frac{x}{6.5} = 3$ is $x=19.5$.