solve the absolute value
3/2x+4/-1=11
// stands for brackets
could someone explain
/2x+7/<=27
/2x+10/>26
/2x-1/=3
I do not understand if someone could help
To solve absolute value equations, you'll need to separate the equation into two separate equations, considering both the positive and negative cases of the absolute value. Here's how you can solve each of the given equations step-by-step:
1. Solve for absolute value equation: |3/2x + 4| / -1 = 11
Step 1: Multiply both sides by -1 to remove the negative sign:
|3/2x + 4| = -11
Step 2: Since an absolute value cannot be negative, this equation has no solution.
2. Solve for absolute value inequality: |2x + 7| ≤ 27
Step 1: Solve for the positive case: 2x + 7 ≤ 27
Subtract 7 from both sides:
2x ≤ 20
Divide by 2:
x ≤ 10
Step 2: Solve for the negative case: -(2x + 7) ≤ 27
Distribute the negative sign:
-2x - 7 ≤ 27
Add 7 to both sides:
-2x ≤ 34
Divide by -2 (remembering to flip the inequality sign):
x ≥ -17
Therefore, the solution to the absolute value inequality |2x + 7| ≤ 27 is -17 ≤ x ≤ 10.
3. Solve for absolute value inequality: |2x + 10| > 26
Step 1: Solve for the positive case: 2x + 10 > 26
Subtract 10 from both sides:
2x > 16
Divide by 2:
x > 8
Step 2: Solve for the negative case: -(2x + 10) > 26
Distribute the negative sign:
-2x - 10 > 26
Add 10 to both sides:
-2x > 36
Divide by -2 (remembering to flip the inequality sign):
x < -18
Therefore, the solution to the absolute value inequality |2x + 10| > 26 is x < -18 or x > 8.
4. Solve for absolute value equation: |2x - 1| = 3
Step 1: Solve for the positive case: 2x - 1 = 3
Add 1 to both sides:
2x = 4
Divide by 2:
x = 2
Step 2: Solve for the negative case: -(2x - 1) = 3
Distribute the negative sign:
-2x + 1 = 3
Subtract 1 from both sides:
-2x = 2
Divide by -2:
x = -1
Therefore, the solution to the absolute value equation |2x - 1| = 3 is x = 2 or x = -1.