To solve the equation [tex]\( |6x + 3| = 21 \)[/tex], follow these steps:
1. Understand the absolute value equation: The equation [tex]\( |6x + 3| = 21 \)[/tex] means that the expression inside the absolute value, [tex]\( 6x + 3 \)[/tex], can be either 21 or -21.
2. Set up two separate equations: This gives us two different linear equations to solve:
- [tex]\( 6x + 3 = 21 \)[/tex]
- [tex]\( 6x + 3 = -21 \)[/tex]
3. Solve the first equation [tex]\( 6x + 3 = 21 \)[/tex]:
- Subtract 3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
6x + 3 - 3 = 21 - 3
\][/tex]
[tex]\[
6x = 18
\][/tex]
- Divide both sides by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{18}{6}
\][/tex]
[tex]\[
x = 3
\][/tex]
4. Solve the second equation [tex]\( 6x + 3 = -21 \)[/tex]:
- Subtract 3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
6x + 3 - 3 = -21 - 3
\][/tex]
[tex]\[
6x = -24
\][/tex]
- Divide both sides by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-24}{6}
\][/tex]
[tex]\[
x = -4
\][/tex]
Therefore, the solutions to the equation [tex]\( |6x + 3| = 21 \)[/tex] are [tex]\( x = 3 \)[/tex] and [tex]\( x = -4 \)[/tex].
Looking at the provided choices:
- A. [tex]\( x = -3 \)[/tex] and [tex]\( x = 4 \)[/tex]
- B. [tex]\( x = -3 \)[/tex] and [tex]\( x = -4 \)[/tex]
- C. [tex]\( x = 3 \)[/tex] and [tex]\( x = -4 \)[/tex]
- D. [tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex]
The correct choice is:
C. [tex]\( x = 3 \)[/tex] and [tex]\( x = -4 \)[/tex].
