Sure! Let's solve the given equation step by step.
The given equation is:
[tex]\[
3x + 4(x + 1) = x + 2(x + 3)
\][/tex]
Step 1: Distribute the constants inside the parentheses.
On the left side of the equation:
[tex]\[
3x + 4(x + 1) = 3x + 4x + 4 = 7x + 4
\][/tex]
On the right side of the equation:
[tex]\[
x + 2(x + 3) = x + 2x + 6 = 3x + 6
\][/tex]
So the equation now is:
[tex]\[
7x + 4 = 3x + 6
\][/tex]
Step 2: Isolate the variable [tex]\(x\)[/tex].
First, subtract [tex]\(3x\)[/tex] from both sides:
[tex]\[
7x + 4 - 3x = 3x + 6 - 3x
\][/tex]
This simplifies to:
[tex]\[
4x + 4 = 6
\][/tex]
Next, subtract 4 from both sides:
[tex]\[
4x + 4 - 4 = 6 - 4
\][/tex]
This simplifies to:
[tex]\[
4x = 2
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex] by dividing both sides by 4:
[tex]\[
x = \frac{2}{4}
\][/tex]
[tex]\[
x = \frac{1}{2}
\][/tex]
Therefore, [tex]\(x\)[/tex] can be simplified and expressed as:
[tex]\[
x = \frac{1}{2}
\][/tex]
So, the numerator and denominator are 1 and 2, respectively. Hence, the value of [tex]\(x\)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
