Question

Which number line represents the solutions to Ix - 5= 1?
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
+
-7 -6 -5 -4 -3 -2 -1 0
1
2
3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2
3 4 5 6 7
o
-7 -6 -5 -4 -3 -2 -1 0 1
3
4 5 6 7
N

Answer 1

The number line that represents the solutions to Ix - 5| = 1 is the number line in the second option.

To solve absolute value equations like |x-5| = 1

We will write that

x - 5 = 1 and x -5 = -1

For the first equation

x - 5 = 1

Add 5 to both sides

x - 5 +5 = 1+5

∴ x = 6

For the second equation

x -5 = -1

Add 5 to both sides as well

x -5 +5 = -1 +5

∴ x = 4

Hence, x = 6 and x = 4

From the image, the second option is dotted (blue) at 4 and 6 on the number line.

Hence, the number line that represents the solutions to Ix - 5| = 1 is the number line in the second option

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