Answer: x=11 and x=-1
Step-by-step explanation:
To solve the equation |x - 5| + 7 = 13, you'll need to isolate the absolute value expression and then solve for x. Here's how:
Subtract 7 from both sides of the equation:
|x - 5| = 13 - 7
|x - 5| = 6
Now, you'll have two cases to consider for the absolute value:
Case 1: (x - 5) = 6
Case 2: (x - 5) = -6
Solve each case separately:
Case 1:
x - 5 = 6
Add 5 to both sides:
x = 6 + 5
x = 11
Case 2:
x - 5 = -6
Add 5 to both sides:
x = -6 + 5
x = -1
So, the solutions to the equation are x = 11 and x = -1.
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Answer: B
Step-by-step explanation:
|x-5|+7=13
subtract 7 from both sides
|x-5|=6
split the simplified problem into two cases
x-5=6 and -(x-5)=6
for x-5=6, add 5 to both sides, x=11.
for -(x-5)=6, distribute the negative sign. -x+5=6. subtract 5: -x=1. then divide by negative one and get x=-1.
Therefore: x=11,-1