Respuesta :

Heather

Answer: D. 3(d + [tex]\frac{5}{3}[/tex]) and 3d + 5

Step-by-step explanation:

       We will distribute and simplify the expressions to find which pair is equivalent. In other words, which pair is equal.

✗ [A] 3(5a + 3) = 15a + 9 ≠ 15a + 6

✗ [B] 2(7b - 2) = 14b - 4 ≠ 14b + 4

✗ [C] 5(2c + 3) = 10c + 15 ≠ 7c + 8

✓ [D] 3(d + [tex]\frac{5}{3}[/tex]) = 3d + 5 = 3d + 5

       3d + 5 = 3d + 5, which means option D is the answer to our question.

Kailes

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

By distributing the multiplication over the addition:

[tex]\leadsto[/tex] A.

• [tex]\small\longrightarrow \sf{3(5a+3)}[/tex]

[tex]\small\longrightarrow \sf{3 \cdot 5a+3 \cdot 3}[/tex]

[tex]\small\longrightarrow \sf{= \underline{15a+9}}[/tex] ✗

[tex]\leadsto[/tex] B.

• [tex]\small\longrightarrow \sf{2(7b-2)}[/tex]

[tex]\small\longrightarrow \sf{2 \cdot 7b-2 \cdot 2}[/tex]

[tex]\longrightarrow \sf{= \underline{14b-4}}[/tex] ✗

[tex]\leadsto[/tex] C.

• [tex]\small\longrightarrow \sf{5(2c+3)}[/tex]

[tex]\small\longrightarrow \sf{=\underline{5 \cdot 2c+ 5 \cdot 3}}[/tex] ✗

[tex]\leadsto[/tex] D.

• [tex]\small\longrightarrow \sf{3(d + \frac{5}{3} ) \: and \: \: 3d + 5}[/tex]

[tex]\small\longrightarrow \sf={\underline{3d+5}}[/tex] [tex]\large\sf{✓}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large \bm{D. \: \: 3(d + \frac{5}{3} ) \: and \: \: 3d + 5}[/tex]

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