To solve the equation [tex]\(2x - 3 + 4x = 21\)[/tex], follow these detailed steps:
### Step 1: Combine Like Terms
First, we need to combine the [tex]\(x\)[/tex] terms on the left side of the equation:
[tex]\[
2x + 4x - 3 = 21
\][/tex]
Combine [tex]\(2x\)[/tex] and [tex]\(4x\)[/tex]:
[tex]\[
6x - 3 = 21
\][/tex]
### Step 2: Isolate the Variable Term
Next, we want to isolate the term with the variable [tex]\(x\)[/tex]. To do this, add 3 to both sides of the equation to get rid of the constant term on the left side:
[tex]\[
6x - 3 + 3 = 21 + 3
\][/tex]
This simplifies to:
[tex]\[
6x = 24
\][/tex]
### Step 3: Solve for [tex]\(x\)[/tex]
Finally, divide both sides of the equation by 6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{24}{6}
\][/tex]
This simplifies to:
[tex]\[
x = 4
\][/tex]
### Conclusion
Thus, the solution to the equation [tex]\(2x - 3 + 4x = 21\)[/tex] is:
[tex]\[
x = 4
\][/tex]
Among the given choices, [tex]\(x = 4\)[/tex] is the correct answer.
