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Natasha_Volkova [10]
3 years ago
9

-2(x+3)<20 Show work and write solution set

Mathematics
1 answer:
Digiron [165]3 years ago
3 0

Answer:

x > - 13

Step-by-step explanation:

Given

- 2(x + 3) < 20 ← distribute parenthesis on left side

- 2x - 6 < 20 ( add 6 to both sides )

- 2x < 26

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

x > - 13

solution set is { x | x > - 13 }

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Answer:

\huge\boxed{f=g(x)\ \text{for}\ x=-\dfrac{16}{3}=-5\dfrac{1}{3}}

Step-by-step explanation:

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?

f(x)=g(x)\iff\dfrac{1}{2}x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\\dfrac{1}{2}x-2x=2x-2x+8\\\\-1\dfrac{1}{2}x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-\dfrac{2\cdot1+1}{2}x=8\\\\-\dfrac{3}{2}x=8\qquad\text{multiply both sides by}\ -\dfrac{2}{3}\\\\\left(-\dfrac{2\!\!\!\!\diagup}{3\!\!\!\!\diagup}\right)\left(-\dfrac{3\!\!\!\!\diagup}{2\!\!\!\!\diagup}x\right)=\left(-\dfrac{2}{3}\right)\cdot8\\\\x=-\dfrac{2\cdot8}{3}\\\\x=-\dfrac{16}{3}

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