Answer:
You can use any real number for x and make the equation true.
Step-by-step explanation:
A system of linear equations occurs when there are (usually) two equations of a line in which same solutions are sought.
A system of linear equations can be in three states: it can have one solution, it can have no solution, or it can have infinite solutions.
A SoLE (system of linear equations) with one solution is probably the most famous one. This means that the lines share an (x,y) coordinate point. When a system of equations with one solution is graphed, they cross at the point.
A SoLE with no solution means that the lines do not share an (x,y) coordinate. When graphed, they do not touch, ever. They can also be considered parallel to one another.
A SoLE with infinite solutions means that the lines always cross at every (x,y) coordinate they emcompass. When graphed, they are literally the same line.
<u>In this case of 4(x+3) = 4x + 12, they are a SoLE with infinite solutions. This is because if I use the distributive property on 4(x+3), the equation then becomes:</u>
4x + 12 = 4x + 12
<u>They are the same thing.</u>
<u>So, if I input an x value, both sides of the equation will always equal each other.</u>
<u>For example, say that I subsitute 0 for x:</u>
4(0 + 3) = 4(0) + 12
4(3) = 12
12 = 12
<u>They equal each other as expected.</u>
<u>Let's take a weirder number to solidify my point, the constant </u><em><u>e</u></em><u>:</u>
4(<em>e</em> + 3) = 4<em>e</em> + 12
4<em>e </em>+ 12 = 4<em>e</em> + 12
<u>Let's even take 1,000,000 as an example:</u>
4(1,000,000 + 3) = 4(1,000,000) + 12
4(1,000,003) = 4,000,000 + 12
4,000,012 = 4,000,012
<u>So yes, this goes to show how religious these SoLE with infinite solutions can be.</u>
