Question

does the equation 3(x + 2) = 4x + 3 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 3 to the x and to the 2. you can think of this as (3 · x) + (3 · 2). rewrite the left side. 3(x + 2) = 4x + 3 + = 4x + 3

Explanation:

Step1: Distribute the 3

Using the distributive property \( a(b + c)=ab + ac \), for \( 3(x + 2) \), we multiply 3 with \( x \) and 3 with 2. So \( 3\times x = 3x \) and \( 3\times2=6 \).
<Expression: \( 3(x + 2)=3x + 6 \)>

Step2: Fill in the boxes

From the distribution, the left - hand side \( 3(x + 2) \) is rewritten as \( 3x+6 \). So the first box should be \( 3x \) and the second box should be \( 6 \).

Answer:

The first box: \( 3x \), The second box: \( 6 \)