solve the equation and then check for extraneous solutions 4(3×+4)=4×+8

Answer 1

To solve the equation, we'll begin by distributing 4 to the terms within the parentheses:
4(3x + 4) = 4x + 8
12x + 16 = 4x + 8

Next, we'll isolate the x terms on one side by subtracting 4x from both sides:
12x - 4x + 16 = 4x - 4x + 8
8x + 16 = 8

Simplifying further, we'll subtract 16 from both sides:
8x + 16 - 16 = 8 - 16
8x = -8

To solve for x, we'll divide both sides by 8:
(8x) / 8 = (-8) / 8
x = -1

Now, let's check for extraneous solutions by substituting x=-1 back into the original equation:
4(3x + 4) = 4x + 8
4(3(-1) + 4) = 4(-1) + 8
4(-3 + 4) = -4 + 8
4(1) = 4
4 = 4

Since the equation remains true when x=-1, there are no extraneous solutions. Therefore, the solution to the equation is x = -1.