7-|m-1|=3
(m-1) or (1-m)
7 - m + 1 = 3
or
7 -1 + m = 3
m = 5
or
m = -3
check
if m = 5
|m-1| = 4
4 = 4 good
if m = -3
|m-1| = 4 good
7 - | m - 1 | = 3 Subtract 3 to both sides
7 - | m - 1 | - 3 = 3 - 3
4 - | m - 1 | = 0 Add | m - 1 | to both sides
4 - | m - 1 | + | m - 1 | = 0 + | m - 1 |
4 = | m - 1 |
| m - 1 | = 4
+ OR - ( m - 1 ) = 4
1 solution :
m - 1 = 4 Add 1 to both s ides
m = - 1 + 1 = 4 + 1
m = 5
2 solution:
- ( m - 1 ) = 4
- m + 1 = 4 Subtract 1 to both sides
- m + 1 - 1 = 4 - 1
- m = 3 Multiply both sides by - 1
m = - 3
The solutions are ;
m = - 3
and
m = 5
To solve the equation 7 - |m - 1| = 3, we need to isolate the absolute value expression and then solve for m by considering two cases.
Here's how you can get started:
Step 1: Eliminate the absolute value by separating the equation into two cases.
Case 1: m - 1 is positive (m - 1 ≥ 0)
In this case, the absolute value is unnecessary, so the equation becomes:
7 - (m - 1) = 3
Case 2: m - 1 is negative (m - 1 < 0)
In this case, the absolute value switches the sign of the expression inside, so the equation becomes:
7 - (-(m - 1)) = 3
Now, let's solve both cases step by step:
Case 1: m - 1 ≥ 0
7 - (m - 1) = 3
Simplify the parentheses:
7 - m + 1 = 3
Combine like terms:
8 - m = 3
Move the variables to one side and the constant terms to the other side:
-m = 3 - 8
-m = -5
Multiply both sides by -1 to isolate m:
m = -5 * -1
m = 5
Case 2: m - 1 < 0
7 - (-(m - 1)) = 3
Distribute the negative sign inside the parentheses:
7 + (m - 1) = 3
Remove the parentheses:
7 + m - 1 = 3
Combine like terms:
m + 6 = 3
Move the constant term to the other side:
m = 3 - 6
m = -3
So the solutions to the equation 7 - |m - 1| = 3 are m = 5 and m = -3.