Question

2. Solve the following inequalities. Graph solutions and write in interval notation. a) 3 - 8x 9 - 4x b) 2y=<7

Answer 1

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Solution: (a) we have, 3-84 > 9-422 STEP 1: Add 4x both side of the equation 43 +3-839-43 +42 =) 3-4> g STEP 2: Add (-3) to both side of the equation (-3) + 3-4 9+(-3) –432 = 6 STEP 3: Multiply both side by -! -) (-1)(4x)- 26-116 =) 43% -6 =) asoo es 312 Hence, solution is 8 € (-∞, -3/ 0,-] Below graph is attached red region is solution of inequality.

20 GRAPH (A) -10 (-1.5, 0) -10 0 10 10- 20

Solution! (b) we have, 2y-g -3 <7 STEP I. Multiply both side by -3 -3(259) > 70-3) 24-9 > -21 STEP 2: Add tg to both side of inequality -) 24-9+9 > - 2179 24 > -12 STEP 3: multiply both side by -) 1124) >(-12) 2 =) Y >-6 Hena, Solution y E (-6.0) Below graph is attached red region is solution inequality

30 GRAPH (B) 20 10 -20 -10 0 10 20 (0, -6) --10 --20 --30