This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hey Dr.Lady, good to see you again. Here are the solutions for the given problems. c) Determine the value of x satisfying |3x - 2| 7. Step 1: Split the absolute value inequality into two separate inequalities. For an inequality of the form |A| B, we have A B or A -B. 3x - 2 7 or 3x - 2 -7 Step 2: Solve the first inequality. 3x - 2 7 3x 7 + 2 3x 9 x (9)/(3) x 3 Step 3: Solve the second inequality. 3x - 2 -7 3x -7 + 2 3x -5 x -(5)/(3) The solution is the union of these two intervals. x -(5)/(3) or x 3 d) Determine the value of x satisfying |x - 1| > 5. Step 1: Split the absolute value inequality into two separate inequalities. For an inequality of the form |A| > B, we have A > B or A < -B. x - 1 > 5 or x - 1 < -5 Step 2: Solve the first inequality. x - 1 > 5 x > 5 + 1 x > 6 Step 3: Solve the second inequality. x - 1 < -5 x < -5 + 1 x < -4 The solution is the union of these two intervals. x < -4 or x > 6 e) Determine the value of x satisfying |x + 3| 7. Step 1: Split the absolute value inequality into two separate inequalities. For an inequality of the form |A| B, we have A B or A -B. x + 3 7 or x + 3 -7 Step 2: Solve the first inequality. x + 3 7 x 7 - 3 x 4 Step 3: Solve the second inequality. x + 3 -7 x -7 - 3 x -10 The solution is the union of these two intervals. x -10 or x 4 f) Determine the value of x satisfying |x + 3| = 4. Step 1: Split the absolute value equation into two separate equations. For an equation of the form |A| = B, we have A = B or A = -B. x + 3 = 4 or x + 3 = -4 Step 2: Solve the first equation. x + 3 = 4 x = 4 - 3 x = 1 Step 3: Solve the second equation. x + 3 = -4 x = -4 - 3 x = -7 The solutions are the two values of x. x = 1 or x = -7 Send me the next one 📸