Question 3 Solve the inequality -3 ≤ 4 -7x/2 ≤ 18
Class X1 - Maths -Linear Inequalities Page 132
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-3 ≤ 4 - 7x/2 ≤ 18
subtract 4 from all sides,
-3 - 4 ≤ 4 - 4 - 7x/2 ≤ 18 -4
-7 ≤ -7x/2 ≤ 14
multiply 2 into all sides,
-7 × 2 ≤ -7x/2 × 2 ≤ 14 × 2
-14 ≤ -7x ≤ 28
divide by (-7) all sides, sign of inequality will be change.
(-14)/(-7) ≥ (-7x)/(-7) ≥ 28/(-7)
2 ≥ x ≥ -4 or -4 ≤ x ≤ 2
hence, x € [ -4 , 2]
subtract 4 from all sides,
-3 - 4 ≤ 4 - 4 - 7x/2 ≤ 18 -4
-7 ≤ -7x/2 ≤ 14
multiply 2 into all sides,
-7 × 2 ≤ -7x/2 × 2 ≤ 14 × 2
-14 ≤ -7x ≤ 28
divide by (-7) all sides, sign of inequality will be change.
(-14)/(-7) ≥ (-7x)/(-7) ≥ 28/(-7)
2 ≥ x ≥ -4 or -4 ≤ x ≤ 2
hence, x € [ -4 , 2]
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