To solve the equation [tex]\(\frac{2x + 3}{6} = \frac{3x + 7}{6}\)[/tex], we can follow these steps:
1. Clear the Denominators:
Since the denominators on both sides of the equation are the same, we can eliminate them by multiplying both sides by 6:
[tex]\[
6 \cdot \frac{2x + 3}{6} = 6 \cdot \frac{3x + 7}{6}
\][/tex]
This simplifies to:
[tex]\[
2x + 3 = 3x + 7
\][/tex]
2. Isolate the Variable:
To solve for [tex]\(x\)[/tex], we need to isolate it on one side of the equation. First, let's subtract [tex]\(2x\)[/tex] from both sides to start simplifying:
[tex]\[
2x + 3 - 2x = 3x + 7 - 2x
\][/tex]
This simplifies to:
[tex]\[
3 = x + 7
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Next, we want to isolate [tex]\(x\)[/tex]. To do this, subtract 7 from both sides:
[tex]\[
3 - 7 = x + 7 - 7
\][/tex]
This simplifies to:
[tex]\[
-4 = x
\][/tex]
4. State the Solution:
Thus, the solution to the given equation is:
[tex]\[
x = -4
\][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\frac{2x + 3}{6} = \frac{3x + 7}{6}\)[/tex] is [tex]\(-4\)[/tex].
