solve
2│2x-7│+11=25
You want to get the absolute value portion of the equation alone first. They you can find what x would equal if it were (2x-7) = blah and if -(2x-7) = blah.
2„ 2x-7„ +11=25
-11 -11
2„ 2x-7„ =14
4x +14 = 14
-14 -14
4x = 0 Divide both by 4
x = 0
Check
2„ 2(0)-7„ +11=25
2„ 0 -7„ +11=25
2„ -7„ +11=25
14 + 11 =25
25 =25
in addition to x=0, x=7
2[2x-7]+11=25
2[2x-7]=14
[2x-7]=7
2x=14
x=7
Check
2[2(7)-7]+11=25
2[7]+11=25
14+11=25
25=25 :D
2│2x-7│+11=25
|2x-7| = 7
then 2x-7 = 7 or -2x + 7 = 7
2x = 14 or 2x = 0
x = 7 or x = 0
To solve the equation 2│2x-7│+11=25, we need to isolate the absolute value expression and then solve for x. Here's how we can do that step by step:
Step 1: Subtract 11 from both sides of the equation.
2│2x-7│ = 25 - 11
2│2x-7│ = 14
Step 2: Divide both sides of the equation by 2.
│2x-7│ = 14/2
│2x-7│ = 7
Step 3: Solve for both the positive and negative cases of the absolute value expression separately.
Case 1: 2x - 7 = 7
Add 7 to both sides:
2x = 7 + 7
2x = 14
Divide both sides by 2:
x = 14/2
x = 7
Case 2: -(2x - 7) = 7
Multiply both sides by -1 to remove the negative sign:
2x - 7 = -7
Add 7 to both sides:
2x = -7 + 7
2x = 0
Divide both sides by 2:
x = 0/2
x = 0
So, the solution to the equation 2│2x-7│+11=25 is x = 7 and x = 0.