Question

does the equation 2(x + 3) = 3x + 4 have one solution, no solutions, or infinitely many solutions? first, lets try to isolate the variable, x. one of the x terms is inside the parentheses on the left. so, lets start by getting rid of the parentheses to make this equation easier to work with. one way to do this is to distribute the 2 to the x and to the 3. you can think of this as (2 · x) + (2 · 3). rewrite the left side. 2(x + 3) = 3x + 4 \square + \square = 3x + 4

Explanation:

Step1: Distribute the 2

To rewrite \(2(x + 3)\), we use the distributive property \(a(b + c)=ab+ac\). Here, \(a = 2\), \(b=x\), and \(c = 3\). So, \(2\times x=2x\) and \(2\times3 = 6\).

Step2: Rewrite the left side

Substitute the distributed terms back. The left side \(2(x + 3)\) becomes \(2x+6\).

Answer:

The first box is \(2x\) and the second box is \(6\), so the left side is \(2x + 6\).