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astraxan [27]
2 years ago
5

Solve fast pls with explanation Marty simplified the expression 2(x - 2) - 2(3) as 2x - 8. Is he correct? Explain why or why not

.
Mathematics
2 answers:
Stells [14]2 years ago
6 0

\\ \sf\longmapsto 2(x-2)-2(3)

  • a(b-c)=ab-ac

\\ \sf\longmapsto 2x-2(2)-6

\\ \sf\longmapsto 2x-4-6

\\ \sf\longmapsto 2x-10

Marty was wrong in opening brackets

Assoli18 [71]2 years ago
3 0

Answer:

  • Marty is incorrect.

Step-by-step explanation:

<u>Let's check his work by simplifying the given expression.</u>

  • 2(x - 2) - 2(3)
  • => 2x - 4 - 6
  • => 2x - 10

When I compare Marty's result and this result, they are un-equal. Hence, Marty is incorrect.

<u>Marty's mistake</u>

  • Marty must've got the problem wrong because of not understanding the distributive property.
  • He probably forgot to multiply -2 by 2. Instead, he only subtracted 2 when he should've subtracted 4 from 2x.
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we have the inequality

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step 1

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\begin{gathered} +(5x+4)\leq10 \\ 5x\leq10-4 \\ 5x\leq6 \\ x\leq\frac{6}{5} \\ x\leq1.20 \end{gathered}

The first solution is all real numbers less than or equal to 1.20

Interval (-infinite,1.20]

step 2

Find out the second solution (negative case)

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Multiply by -1 both sides

\begin{gathered} (5x+4)\ge-10 \\ 5x\ge-10-4 \\ 5x\ge-14 \\ x\ge-\frac{14}{5} \\ x\ge-2.8 \end{gathered}

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step 3

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The solution is

[-2.8, infinite) ∩ (-infinite,1.20]=[-2.8,1.20]

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see the attached figure to better understand the problem

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