Question

Solve 3 – 4x < x – 12, x ∈ { -1, 0, 1, 2, 3, 4, 5, 6, 7}​

Answer 1

Answer:

{4,5,6,7}

Step-by-step explanation:

3-4x < x-12

=> 3+12 < x+4x

=> 5x > 15 (by reversing)

=> x > 3

so, x ∈ {4, 5, 6, 7}

Answer 2

Answer:

$\texttt\pink{x = - 1}$

$\texttt\pink{3-4(-1) < -1-12}$

$\texttt\pink{3+4 < -13}$

$\texttt\pink{7 < -13}$

$\texttt\pink{The above statement is false}$

$\texttt\blue{x = 0}$

$\texttt\blue{3-4(0) < 0-12}$

$\texttt\blue{3 - 0 < -12}$

$\texttt\blue{3 < -12}$

$\texttt\blue{The above statement is false}$

$\texttt\orange{x = 1}$

$\texttt\orange{3 - 4(1) < 1- 12}$

$\texttt\orange{3-4 < -11}$

$\texttt\orange{-1 < -11}$

$\texttt\orange{The above statement is false}$

$\texttt\green{x = 2}$

$\texttt\green{3 - 4(2) < 2-12}$

$\texttt\green{3-8 < -10}$

$\texttt\green{-5 < -10}$

$\texttt\green{The above statement is false}$

$\texttt\purple{x = 3}$

$\texttt\purple{3 -4(3) < 3-12}$

$\texttt\purple{3-12 < -9}$

$\texttt\purple{-9 < -9}$

$\texttt\purple{The above statement is false}$

$\texttt\red{x = 4}$

$\texttt\red{3 -4(4) < 4-12}$

$\texttt\red{3 - 16 < -8}$

$\texttt\red{-13 < -8}$

$\texttt\red{The above statement is True}$

$\texttt\pink{x = 5}$

$\texttt\pink{3 - 4(5) < 5-12}$

$\texttt\pink{3 - 20 < -7}$

$\texttt\pink{-17 < -7}$

$\texttt\pink{The above statement is True}$

$\texttt\orange{x = 6}$

$\texttt\orange{3 - 4(6) < 6-12}$

$\texttt\orange{3 - 24 < -6}$

$\texttt\orange{-21 < -6}$

$\texttt\orange{The above statement us True}$

$\texttt\blue{x = 7}$

$\texttt\blue{3-4(7) < 7-12}$

$\texttt\blue{3 - 28 < -5}$

$\texttt\blue{-25 < -5}$

$\texttt\blue{The above statement us True}$

$\mathsf\green{The \: values \: which \: were \: satisfied \: were \: (4,5,6,7)}$

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