Example 3: Solve |c 7| = |2c 2|. – – Step 1: Let the expression on one Done, because the expression on the side of the equation consist only of a left already consists only of a single single absolute value expression. absolute value expression. Step 2: Is the number on the other No, because |2c 2| is surely not – side of the equation negative? negative (the absolute value of a number can never be negative). Proceed to Step 3. Step 3: To satisfy the equation, the c 7 = +(2c 2) c 7 = 2) – – – –(2c – expression inside the first absolute value, 7, can either be +(2c 2) or c – – 2). These correspond to two –(2c – equations. [Notice the similarity to Step 3 of Example 1.] Step 4: Solve both equations. c 7 = +(2c 2) c 7 = 2) – – – –(2c – c 7 = 2c 2 c 7 = + 2 – – – –2c 7 = 3c 7= 2 –c – –2 – = 5 3c = 9 –c c = c = 3 –5 Again, we can check that these two values for c satisfy the original equation. Example 4: Solve |b + 2| = |b 3| – Step 1: Let the expression on one Done, because the expression on the side of the equation consist only of a left already consists only of a single single absolute value expression. absolute value expression. Is the number on the other No, because |b 3| is surely Step 2: not – side of the equation negative? negative (the absolute value of a number can never be negative). Proceed to Step 3. Step 3: To satisfy the equation, the b + 2 = +(b 3) b + 2 = 3) – –(b – expression inside the first absolute value, b + 2, can either be equal to +(b 3) or 3). These – –(b – correspond to two equations. [Notice the similarity to Step 3 of Example 1.]
Example 3: Solve |c – 7| = |2c – 2|. Step 1: Let the expression on one side of the equation consist only of a single absolute value expression. Done, because the expression on the left already consists only of a single absolute value expression. Step 2: Is the number on the other side of the equation negative? No, because |2c – 2| is surely not negative (the absolute value of a number can never be negative). Proceed to Step 3. Step 3: To satisfy the equation, the expression inside the first absolute value, c – 7, can either be +(2c – 2) or –(2c – 2). These correspond to two equations. [Notice the similarity to Step 3 of Example 1.] c – 7 = +(2c – 2) c – 7 = –(2c – 2) Step 4: Solve both equations. c – 7 = +(2c – 2) c – 7 = 2c – 2 –c – 7 = –2 –c = 5 c = –5 c – 7 = –(2c – 2) c – 7 = –2c + 2 3c – 7= 2 3c = 9 c = 3 Again, we can check that these two values for c satisfy the original equation. Example 4: Solve |b + 2| = |b – 3| Step 1: Let the expression on one side of the equation consist only of a single absolute value expression. Done, because the expression on the left already consists only of a single absolute value expression. Step 2: Is the number on the other side of the equation negative? No, because |b – 3| is surely not negative (the absolute value of a number can never be negative). Proceed to Step 3. Step 3: To satisfy the equation, the expression inside the first absolute value, b + 2, can either be equal to +(b – 3) or –(b – 3). These correspond to two equations. [Notice the similarity to Step 3 of Example 1.] b + 2 = +(b – 3) b + 2 = –(b – 3)
7-math-lm_mod3.docx