Question

6) x|-1=-5; 8) 5|x| + 1 = 0 208 7) 2|x|-5=0; 9) |5x + 3| - 3 = 0 10) |3x - 2| + 5 = 7 9) |5x + 3| - 3 = 0 8) 5|x| + 1 = 0 208 7) 2|x|-5=0; 6) x|-1=-5; 5) |x| + 3 = 9 ; 4) |x + 4| = - 3 ; 3) |x - 3| = 0 ; 2) |x+2|=3; 1) |x|=7;

Answer 1

.............................

Answer 2

1) |x| = 7 To solve this equation, we need to consider two cases: when x is positive and when x is negative.

Case 1: x is positive In this case, |x| = x. So the equation becomes x = 7. The solution is x = 7.

Case 2: x is negative In this case, |x| = -x. So the equation becomes -x = 7. Multiplying both sides by -1 gives x = -7. The solution is x = -7.

Therefore, the solutions to the equation |x| = 7 are x = 7 and x = -7.

2) |x + 2| = 3 Again, we need to consider two cases: when x + 2 is positive and when x + 2 is negative.

Case 1: x + 2 is positive In this case, |x + 2| = x + 2. So the equation becomes x + 2 = 3. Subtracting 2 from both sides gives x = 1. The solution is x = 1.

Case 2: x + 2 is negative In this case, |x + 2| = -(x + 2). So the equation becomes -(x + 2) = 3. Multiplying both sides by -1 gives x + 2 = -3. Subtracting 2 from both sides gives x = -5. The solution is x = -5.

Therefore, the solutions to the equation |x + 2| = 3 are x = 1 and x = -5.

3) |x - 3| = 0 In this case, the absolute value of any number is always non-negative. The only way for the absolute value to be equal to 0 is if the number inside the absolute value is 0. So the equation becomes x - 3 = 0. Adding 3 to both sides gives x = 3. The solution is x = 3.

Therefore, the solution to the equation |x - 3| = 0 is x = 3.

4) |x + 4| = -3 Since the absolute value is always non-negative, it can never be equal to a negative number. Therefore, there are no solutions to the equation |x + 4| = -3.

5) |x + 3| = 9 Again, we consider two cases: when x + 3 is positive and when x + 3 is negative.

Case 1: x + 3 is positive In this case, |x + 3| = x + 3. So the equation becomes x + 3 = 9. Subtracting 3 from both sides gives x = 6. The solution is x = 6.

Case 2: x + 3 is negative In this case, |x + 3| = -(x + 3). So the equation becomes -(x + 3) = 9. Multiplying both sides by -1 gives x + 3 = -9. Subtracting 3 from both sides gives x = -12. The solution is x = -12.

Therefore, the solutions to the equation |x + 3| = 9 are x = 6 and x = -12.

6) x - 1 = -5 To solve this equation, we can simply add 1 to both sides to isolate x. This gives x = -4. The solution is x = -4.

Therefore, the solution to the equation x - 1 = -5 is x = -4.