Variable Equation Giver: 4x-1=4(x+3) Mep 11 4x-1=4x+12 Mep 21 4x-1=4x+4x+12-4x Mep 3: -1=12 4x Consikler the given equation and its s solution. Which property is 4 A Substitution 4x B Additive inverse 4x C Identity Property 4 D Muliplicative trverse 4x According to Step 3, the given equation has how many solutions? 4x A 1 solution 4x B 2 solutions 4x C no solution 4x D infintely many solutions

## Step 1<br />The given equation is \(4x - 1 = 4(x + 3)\). This equation is solved by applying the distributive property on the right side of the equation.<br /><br />## Step 2<br />The distributive property is applied to the right side of the equation, which results in \(4x - 1 = 4x + 12\).<br /><br />## Step 3<br />The next step is to isolate the variable \(x\) on one side of the equation. This is done by subtracting \(4x\) from both sides of the equation, which gives \(-1 = 12\).<br /><br />## Step 4<br />The equation \(-1 = 12\) is a contradiction, which means it is not possible for this equation to be true. Therefore, the given equation has no solution.<br /><br />## Step 5<br />The property used in Step 3 is the additive inverse. The additive inverse of a number is the number that, when added to the original number, equals zero. In this case, \(4x\) is subtracted from both sides of the equation, which is the same as adding \(-4x\) to both sides.