Sure, let's solve the equation step-by-step: [tex]\(\frac{15}{4} - 7x = 9\)[/tex].
1. Isolate the term with the variable [tex]\(x\)[/tex]:
Start by subtracting [tex]\(\frac{15}{4}\)[/tex] from both sides of the equation.
[tex]\[
-7x = 9 - \frac{15}{4}
\][/tex]
2. Simplify the right side of the equation:
To combine the terms on the right side, convert 9 into a fraction with a common denominator:
[tex]\[
9 = \frac{36}{4}
\][/tex]
Now, subtract the fractions:
[tex]\[
9 - \frac{15}{4} = \frac{36}{4} - \frac{15}{4} = \frac{36 - 15}{4} = \frac{21}{4}
\][/tex]
Therefore, the equation becomes:
[tex]\[
-7x = \frac{21}{4}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by [tex]\(-7\)[/tex]:
[tex]\[
x = \frac{\frac{21}{4}}{-7}
\][/tex]
4. Simplify the division:
When dividing by a fraction, you multiply by its reciprocal. Thus:
[tex]\[
x = \frac{21}{4} \times \frac{1}{-7} = \frac{21 \times 1}{4 \times -7} = \frac{21}{-28} = -\frac{3}{4}
\][/tex]
So, the solution to the equation [tex]\(\frac{15}{4} - 7x = 9\)[/tex] is:
[tex]\( x = -\frac{3}{4} \)[/tex].
Hence, the correct answer is:
(b) [tex]\(-\frac{3}{4}\)[/tex].
