1. **Stating the problem:** We are given several algebraic expressions and word problems involving variables and constants. We need to simplify expressions and write algebraic expressions for purchases. 2. **Simplifying expressions:** - For 18. $2x + 4y$ is already simplified. - For 22. Simplify each option: a. $2(2x - 6) = 4x - 12$ b. $2(2x - 4) = 4x - 8$ c. $x - 8 + 3x = 4x - 8$ - For 23. Simplify each option: a. $9.6x - 15$ (already simplified) b. $30x - 7$ (already simplified) c. $4(3x - 8) = 12x - 32$ 3. **Writing algebraic expressions for purchases:** - a. Mr. Tonkery bought $x$ soccer balls and 3 baseballs. Each soccer ball costs 15 (from the graph label). The expression is: $$15x + 3$$ - b. Dennis, Eddie, and Felix each bought a baseball and $x$ pairs of sweat socks. Assuming the cost of baseballs and socks is not given, the expression is: $$3(1 + x) = 3 + 3x$$ 4. **Checking equivalence of expressions from Exercise 25:** - Expression a: $15x + 3$ - Expression b: $3 + 3x$ Are they equivalent? No, because $15x + 3$ and $3 + 3x$ are not equal unless $15x = 3x$, which implies $x=0$. So generally, they are not equivalent. **Final answers:** - Simplified expressions for 22: b and c simplify to $4x - 8$ - Simplified expressions for 23: a is $9.6x - 15$, b is $30x - 7$, c is $12x - 32$ - Algebraic expressions for purchases: a) $15x + 3$, b) $3 + 3x$ - Expressions are not equivalent unless $x=0$.