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MATH 1010-2: Quiz 3A Solution 1. (4 points) Solve the inequality and sketch the solution on the real number line: −3x + 4 > 2x + 9 Solution: −3x + 4 − 2x > 2x + 9 − 2x −5x + 4 > 9 −5x + 4 − 4 > 9 − 4 −5x > 5 1 − 5 (−5x) < − 15 × 5 x < −1 b b -3 -2 )b -1 b b b b 0 1 2 3 2. (3 points) Solve the equation: |x + 1| = 4 Solution: (a) We are going to find solutions among real numbers greater than or equal to −1. In this case, x + 1 is always positive or 0. So it’s always true that |x + 1| = x + 1. The original equation becomes x+1=4 whose solution is x = 3. Since 3 > −1, it’s in the area that we are finding solutions. (b) We are going to find solutions among real numbers less than −1. In this case, x + 1 is always negative. So it’s always true that |x + 1| = −(x + 1). The original equation becomes −(x + 1) = 4 whose solution is x = −5. Since −5 < −1, it’s in the area that we are finding solutions. To conclude, there are two solutions of this equation. They are 3 and −5. 3. (3 points) Plot (3,1) on a rectangular coordinate system. y 3 2 1 b b b 0 (3,1) b b b b b 1 2 3 x MATH 1010-2: Quiz 3B Solution 1. (4 points) Solve the inequality and sketch the solution on the real number line: −2x + 3 > x + 9 Solution: −2x + 3 − x > x + 9 − x −3x + 3 > 9 −3x + 3 − 3 > 9 − 3 −3x > 6 1 − 3 (−3x) < − 13 × 6 x < −2 b -3 )b -2 b b b b b -1 0 1 2 3 2. (3 points) Solve the equation: |x + 1| = 3 Solution: (a) We are going to find solutions among real numbers greater than or equal to −1. In this case, x + 1 is always positive or 0. So it’s always true that |x + 1| = x + 1. The original equation becomes x+1=3 whose solution is x = 2. Since 2 > −1, it’s in the area that we are finding solutions. (b) We are going to find solutions among real numbers less than −1. In this case, x + 1 is always negative. So it’s always true that |x + 1| = −(x + 1). The original equation becomes −(x + 1) = 3 whose solution is x = −4. Since −4 < −1, it’s in the area that we are finding solutions. To conclude, there are two solutions of this equation. They are 2 and −4. 3. (3 points) Plot (3,2) on a rectangular coordinate system. y 3 2 1 b b b b 0 (3,2) b b b b 1 2 3 x