Question

start by subtracting 3x from both sides. what remains on each side of the equation? 3x + 8 = 4 + 3x - 3x - 3x 8 = 4 what does the statement 8 = 4 tell you about the original equation? 8 = 4 is a? statement. for any value of x, the original equation is?.

Explanation:

Step1: Analyze the equation manipulation

We start with the equation \(3x + 8=4 + 3x\). When we subtract \(3x\) from both sides, on the left - hand side: \((3x + 8)-3x=3x - 3x+8 = 8\). On the right - hand side: \((4 + 3x)-3x=4+3x - 3x = 4\). So we get \(8 = 4\).

Step2: Determine the type of statement \(8 = 4\)

A statement of the form \(a=b\) is true if \(a\) and \(b\) have the same value and false otherwise. Since \(8
eq4\), the statement \(8 = 4\) is a false statement.

Step3: Analyze the original equation

If we try to solve the original equation \(3x+8 = 4 + 3x\), we can subtract \(3x\) from both sides as we did before. We end up with a false statement. This means that there is no value of \(x\) that will make the original equation true. So for any value of \(x\), the original equation is false (or has no solution).

Answer:

The first blank: false; The second blank: false (or has no solution)