Solve each of the following equations. Show its solution set on a number line.
I4x-4(x+1)I=4
We first simplify the absolute value expression by distributing the negative sign inside the absolute value brackets:
I4x-4(x+1)I = I4x-4x-4I = I-4I = I-4I = 4
Now we can solve for x by considering two cases:
Case 1: 4x-4(x+1) = 4
Simplifying, we get:
4x - 4x - 4 = 4
-4 = 4
This equation has no solutions, so we discard this case.
Case 2: -(4x-4(x+1)) = 4
Simplifying, we get:
-4x + 4(x+1) = 4
4 = 4
This equation is true for all values of x, so we have infinitely many solutions.
To show this on a number line, we can draw an arrow that extends from negative infinity to positive infinity, since every value of x satisfies the equation.
Solution set: (-∞, ∞)