Question

10.which two expressions are equivalent?
a. 9(6 + x) and 9 · 6+ 9 · x
b. x + (8 · 9) and (x + 8) · 9
c. 8· 6 ÷ x and 8 · x ÷ 6
d. 6 · x + 3 and 6 · (x + 3)

Explanation:

Step1: Analyze Option a

Apply distributive property: $9(6+x) = 9\cdot6 + 9\cdot x$

Step2: Analyze Option b

Simplify both expressions:
Left: $x+(8\cdot9)=x+72$
Right: $(x+8)\cdot9=9x+72$, not equivalent.

Step3: Analyze Option c

Simplify both expressions:
Left: $8\cdot6\div x=\frac{48}{x}$
Right: $8\cdot x\div6=\frac{8x}{6}=\frac{4x}{3}$, not equivalent.

Step4: Analyze Option d

Simplify right expression:
$6\cdot(x+3)=6x+18$, left is $6x+3$, not equivalent.

Answer:

a. $9(6 + x)$ and $9 \cdot 6+ 9 \cdot x$