# Given: A = {18, 6, −3, −12}Determine all elements of set A that are in the solution of the inequality (2/3)x+3<-2x-7

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We are given A = {18, 6, -3, -12} and asked to find which values from the given set satisfy the inequality (2/3)x + 3 < -2x - 7.

We solve the inequality.

=> (2/3)x + 3 < -2x -7

=> (2/3)x +3 -3 < -2x -7 -3

=> (2/3)x < -2x -10

=> (2/3)x + 2x < -10

=> (8/3)x < -10

=> x < -30/8

Simplifying we find that x < -15/4.

The only member of the given solution set which satisfies the inequality is -12.

justaguide | College Teacher | (Level 2) Distinguished Educator

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We have the inequality: (2/3)x + 3 < -2x -7

Substitute the values from the given set A = {18, 6, -3, -12}

x = 18 : (2/3)*18 + 3 = 15, -2*18 - 7 = -43

15 > -43, inequality not satisfied

x = 6: (2/3)*6 + 3 = 7, -2*6 - 7 = -19

7 > -19, inequality not satisfied

x = -3: (2/3)*(-3) + 3 = 1, -2*(-3) - 7 = -1

1 > -1, inequality not satisfied

x = -12 : (2/3)*(-12) + 3 = -5, -2*(-12) - 7 = 17

-5 < 17, inequality satisfied

The only solution is x = -12