Sure! Let's solve each of these equations step by step.
### 1. Solving [tex]\(\frac{3}{4} x = 9\)[/tex] for [tex]\(x\)[/tex]:
First, isolate [tex]\(x\)[/tex]:
[tex]\[
\frac{3}{4} x = 9
\][/tex]
Multiply both sides by [tex]\(\frac{4}{3}\)[/tex] to get [tex]\(x\)[/tex] alone:
[tex]\[
x = 9 \times \frac{4}{3}
\][/tex]
Simplifying the right side:
[tex]\[
x = 12
\][/tex]
### 2. Solving [tex]\(a + x = b\)[/tex] for [tex]\(x\)[/tex]:
We need to express [tex]\(x\)[/tex] in terms of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
a + x = b
\][/tex]
Subtract [tex]\(a\)[/tex] from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x = b - a
\][/tex]
### 3. Solving [tex]\(c x = d\)[/tex] for [tex]\(x\)[/tex]:
We need to express [tex]\(x\)[/tex] in terms of [tex]\(c\)[/tex] and [tex]\(d\)[/tex]:
[tex]\[
c x = d
\][/tex]
Divide both sides by [tex]\(c\)[/tex] to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{d}{c}
\][/tex]
### 4. Solving [tex]\(a + 5 x = 7 x - r\)[/tex] for [tex]\(r\)[/tex]:
First, let's simplify and isolate [tex]\(r\)[/tex]:
[tex]\[
a + 5 x = 7 x - r
\][/tex]
Subtract [tex]\(5 x\)[/tex] from both sides:
[tex]\[
a = 7 x - 5 x - r
\][/tex]
Which simplifies to:
[tex]\[
a = 2 x - r
\][/tex]
Add [tex]\(r\)[/tex] to both sides:
[tex]\[
a + r = 2 x
\][/tex]
Subtract [tex]\(a\)[/tex] from both sides to isolate [tex]\(r\)[/tex]:
[tex]\[
r = 2 x - a
\][/tex]
### Summary:
Combining all these results, we get:
1. [tex]\( x = 12 \)[/tex]
2. [tex]\( x = b - a \)[/tex]
3. [tex]\( x = \frac{d}{c} \)[/tex]
4. [tex]\( r = 2 x - a \)[/tex]
So, the solutions to the given equations are:
[tex]\[
(x, x \text{ in terms of } a \text{ and } b, x \text{ in terms of } c \text{ and } d, r \text{ in terms of } a \text{ and } x) = (12, b - a, \frac{d}{c}, 2x - a)
\][/tex]
