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3 years ago

Part A: Consider the equation x + 7 = 16. Which number from the set {5, 7, 9, 11} makes the equation true?

Mathematics

1 answer:

wel3 years ago

3 0

Part A: Substitute/plug in each number into the equation to see which number will make the equation true.

x + 7 = 16 Plug in 5 into "x"

5 + 7 = 16

12 = 16 5 doesn't make the equation true because it equals 12 not 16

x + 7 = 16 Plug in 7 into "x"

7 + 7 = 16

14 = 16 7 doesn't make the equation true because it equals 14 not 16

x + 7 = 16 Plug in 9 into "x"

9 + 7 = 16

16 = 16 9 makes the equation true because it equals 16

Part B: Plug in 9 into "x" in the inequality to see if it still makes it true.

x + 7 < 16 [x plus 7 is less than 16]

9 + 7 < 16

16 < 16 [16 is less than 16] The same number would not make the inequality true because 16 can't be less than itself.

To figure out which numbers satisfy the inequality, plug it into the inequality:

x + 7 < 16 Plug in 5 into "x"

5 + 7 < 16

12 < 16 5 does satisfy the inequality because 12 is less than 16

x + 7 < 16 Plug in 7 into "x"

14 < 16 7 does satisfy the inequality because 14 is less than 16

x + 7 < 16 Plug in 11 into "x"

11 + 7 < 16

18 < 16 11 doesn't satisfy the inequality because 18 isn't less than 16

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Step-by-step explanation:

METHOD 1.

We know:

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METHOD 2.

$\text{Find}\ f^{-1}(x)$

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exchange x to y and vice versa:

$x=3y+12$

solve for y:

$3y+12=x$ subtract 12 from both sides

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$f\bigg(f^{-1}(x)\bigg)\to$ replace x in f(x) with the expression $\dfrac{x-12}{3}$

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METHOD 3.

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