For each value of w , determine whether it is a solution to 6=(w)/(4)-1 . multirow(2)(*)( w ) & multicolumn(2)(|c|)( Is it a solution? ) cline ( 2 - 3 ) & Yes & No 40 & & 28 & & -16 & & -4 & &

We are tasked with determining whether each value of \( w \) satisfies the equation \( 6 = \frac{w}{4} - 1 \). To do this, we will substitute each given value of \( w \) into the equation and check if the left-hand side equals the right-hand side.<br /><br />## Step 1: Rearrange the equation<br />The given equation is:<br />\[<br />6 = \frac{w}{4} - 1<br />\]<br />To simplify, add \( 1 \) to both sides:<br />\[<br />6 + 1 = \frac{w}{4}<br />\]<br />\[<br />7 = \frac{w}{4}<br />\]<br />Now, multiply both sides by \( 4 \) to isolate \( w \):<br />\[<br />w = 7 \times 4<br />\]<br />\[<br />w = 28<br />\]<br />Thus, the solution to the equation is \( w = 28 \).<br /><br />## Step 2: Check each value of \( w \)<br />We will now substitute each given value of \( w \) into the original equation \( 6 = \frac{w}{4} - 1 \) to determine if it satisfies the equation.<br /><br />### Substitution for \( w = 40 \):<br />Substitute \( w = 40 \) into the equation:<br />\[<br />6 = \frac{40}{4} - 1<br />\]<br />Simplify:<br />\[<br />6 = 10 - 1<br />\]<br />\[<br />6 \neq 9<br />\]<br />Thus, \( w = 40 \) is **not** a solution.<br /><br />### Substitution for \( w = 28 \):<br />Substitute \( w = 28 \) into the equation:<br />\[<br />6 = \frac{28}{4} - 1<br />\]<br />Simplify:<br />\[<br />6 = 7 - 1<br />\]<br />\[<br />6 = 6<br />\]<br />Thus, \( w = 28 \) **is** a solution.<br /><br />### Substitution for \( w = -16 \):<br />Substitute \( w = -16 \) into the equation:<br />\[<br />6 = \frac{-16}{4} - 1<br />\]<br />Simplify:<br />\[<br />6 = -4 - 1<br />\]<br />\[<br />6 \neq -5<br />\]<br />Thus, \( w = -16 \) is **not** a solution.<br /><br />### Substitution for \( w = -4 \):<br />Substitute \( w = -4 \) into the equation:<br />\[<br />6 = \frac{-4}{4} - 1<br />\]<br />Simplify:<br />\[<br />6 = -1 - 1<br />\]<br />\[<br />6 \neq -2<br />\]<br />Thus, \( w = -4 \) is **not** a solution.<br /><br />## Step 3: Fill in the table<br />Based on our calculations, we can now complete the table as follows:<br /><br />\[<br />\begin{array}{|c|c|c|}<br\ />\hline\ <br\ />\ w\ \ &\ Yes\ &\ No\ \\<br\ />\hline\ <br\ />40\ &\ &\ X\ \\<br\ />\hline\ <br\ />28\ &\ X\ &\ \\<br\ />\hline\ <br\ />-16\ &\ &\ X\ \\<br\ />\hline\ <br\ />-4\ &\ &\ X\ \\<br\ />\hline<br\ />\end{array}<br />\]