Question

w solution? 0 not a solution 1 not a solution 2 not a solution 3 not a solution 40 the value of w + 3 is always 3 more than the value of w. that means the value of w + 3 will never equal the value of w. 41 how many solutions does the equation have? explain. 42 there are? values of w that make the equation true. the equation has?

Explanation:

Step1: Analyze the equation

The equation here is implied to be \( w + 3=w \) (since we are comparing \( w + 3 \) and \( w \)). Let's try to solve it algebraically. Subtract \( w \) from both sides: \( w+3 - w=w - w \), which simplifies to \( 3 = 0 \). This is a contradiction.

Step2: Interpret the contradiction

A contradiction like \( 3 = 0 \) means that there are no values of \( w \) that will satisfy the equation \( w + 3=w \). Also, from the reasoning given, \( w + 3 \) is always 3 more than \( w \), so they can never be equal. The table also shows that for \( w = 0,1,2,3 \), none are solutions, and algebraically we see no solution exists.

Answer:

The equation has 0 solutions. Because when we try to solve \( w + 3=w \), we get \( 3 = 0 \) (a contradiction), and also \( w + 3 \) is always 3 greater than \( w \), so no value of \( w \) can make \( w + 3 \) equal to \( w \). There are 0 values of \( w \) that make the equation true.