To solve the equation [tex]\(6x + 3 = 4x + 11\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Isolate the variable terms on one side of the equation:
Start by getting all the terms with [tex]\(x\)[/tex] on one side of the equation and the constant terms on the other side. You can do this by subtracting [tex]\(4x\)[/tex] from both sides:
[tex]\[
6x + 3 - 4x = 4x + 11 - 4x
\][/tex]
Simplify both sides:
[tex]\[
2x + 3 = 11
\][/tex]
2. Isolate the constant term:
Next, we need to isolate [tex]\(2x\)[/tex] by getting rid of the constant term on the left side. Subtract 3 from both sides:
[tex]\[
2x + 3 - 3 = 11 - 3
\][/tex]
Simplify both sides:
[tex]\[
2x = 8
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Finally, solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{8}{2}
\][/tex]
Simplify:
[tex]\[
x = 4
\][/tex]
Therefore, the solution to the equation [tex]\(6x + 3 = 4x + 11\)[/tex] is [tex]\(x = 4\)[/tex].
