To solve the equation [tex]\(4x^2 - 3 = 1\)[/tex], we need to isolate [tex]\(x^2\)[/tex] first:
1. Start with the given equation:
[tex]\[
4x^2 - 3 = 1
\][/tex]
2. Add 3 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
4x^2 - 3 + 3 = 1 + 3
\][/tex]
[tex]\[
4x^2 = 4
\][/tex]
3. Divide both sides by 4 to solve for [tex]\(x^2\)[/tex]:
[tex]\[
\frac{4x^2}{4} = \frac{4}{4}
\][/tex]
[tex]\[
x^2 = 1
\][/tex]
4. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \pm1
\][/tex]
So, the possible values for [tex]\(x\)[/tex] are 1 and -1.
Next, we need to determine the value of [tex]\(1 - 2\)[/tex] for each solution of [tex]\(x\)[/tex]:
5. For [tex]\(x = 1\)[/tex]:
[tex]\[
1 - 2 = -1
\][/tex]
6. For [tex]\(x = -1\)[/tex]:
[tex]\[
-1 - 2 = -3
\][/tex]
Thus, the values of [tex]\(1 - 2\)[/tex], given the solutions to the equation, are -1 and -3. Hence, the right answer among the given options for a value of [tex]\(1 - 2\)[/tex] corresponding to the computed [tex]\(x\)[/tex] values is:
[tex]\[
(a) -1
\][/tex]
So the correct choice is:
[tex]\[
(a) -1
\][/tex]
