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3 years ago

1. Solve -21 < -3x + 6 < 12

Mathematics

1 answer:

guapka [62]3 years ago

5 0

Answer:

-2<x<9

Step-by-step explanation:

−21<−3x+6<12-21<-3x+6<12

Move all terms not containing xx from the center section of the inequality.

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−27<−3x<6-27<-3x<6

Divide each term in the inequality by −3-3.

−27−3>−3x−3>6−3-27-3>-3x-3>6-3

Divide −27-27 by −3-3.

9>−3x−3>6−39>-3x-3>6-3

Cancel the common factor of −3-3.

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9>x>6−39>x>6-3

Divide 66 by −3-3.

9>x>−29>x>-2

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

−2<x<9-2<x<9

The result can be shown in multiple forms.

Inequality Form:

−2<x<9-2<x<9

Interval Notation:

(−2,9)

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Answer:

$10 + (\frac{2}{3}) a = 50$ is the CORRECT equation.

Step-by-step explanation:

The given question is INCOMPLETE.

Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.” Javier writes the equation { 10 + 2/3} where a is the tree’s age in years. His equation is not correct. What error did he make?

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a: The tree’s age in years.

Also, “The sum of 10 and two-thirds of that tree’s age, in years, is equal to 50.”

⇒ 10 + two-thirds of that tree’s age = 50

$\implies 10 + (\frac{2}{3}) a = 50$

But in the equation written by Javier, the the third fraction is NOT MULTIPLIED by the age of the tree a in Years.

So, the written equation by Javier is Incorrect.

Now, solving the written correct equation for the value of a, we get:

$\implies 10 + (\frac{2}{3}) a = 50\\\implies (\frac{2}{3}) a = 40\\\implies a = 40 \times (\frac{3}{2}) = 60\\\implies a = 60$

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3 years ago