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Which value of X is in the solution set of the inequality 36X+7<16?

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Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

Solution set involves the range of all values of x that satisfy to the inequality, not just one single x as it is for a linear equation. Rewrite the inrquality by subtracting 7 from both sides of it. This is an equivalent operation that doesn't chnage in the solution of the ineqaulity. We will obtain   36x < 9. Then divide both sides by 36 to get  x < 1/4 (dividing by a positive number doesn't change the sign of the inequality). Thus, x < 1/4 involves all values of the variable x that lay on the left from 1/4 on a number line, and this is your set. Because the sign of the ineqaulity is "strictly less", the point "x =1/4" can't be included into the range.