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QN 1: Find the smallest integer that satisfy the inequality
3x + 7 ≤ 7x + 9
SOLUTION
3x +7 ≤ 7x + 9
3x – 7x ≤ 9 – 7 (collecting like terms)
-4x ≤ 2
-4x/-4 ≥ 2/-4 (divide both sides by -4)
X ≥ -1/2
But x is an integer
ie x= {0,1,2,3………}
therefore, the required smallest integer is 0
Remember that
. When both sides of an inequality are multiplied or divided by the same negative number, the direction of the inequality is reversed.
i.e. if 6<9, then 6/-3>9/-3 or -2>-3
. Integer is the positive or negative number with no fractional or decimal
I.e.{ … -2,-1,0,1,2…} are integers
{ -1.5, -1/4,1/2} are not integers
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