EXAMPLE 9 Solve: -4 < 2(x – 1) S 4. Write the solution set in interval notation and graph it. Strategy We will use properties of inequality to isolate the variable by itself as the middle part of the inequality. Why To solve the original inequality, we want to find a simpler equivalent inequality of the form a number < xs a number, whose solution is obvious. Solution -4 < 2(x – 1)S 4 -4 < 2x - This is the compound inequality to solve. Distribute the multiplication by 2. -4 + 2 < 2x - + 2 5 4 + 2 To isolate 2x, undo the subtraction of 2 by adding 2 to all three parts. < 2x S 6 Do the additions. 2x To isolate x, we undo the multiplication by 2 by dividing all three parts by 2. 2 2 2 O

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