Certainly! Let's solve the equation step-by-step.
Consider the equation:
[tex]\[ -2(bx - 5) = 16 \][/tex]
### Solving for [tex]\(x\)[/tex] in terms of [tex]\(b\)[/tex]:
1. Distribute -2 on the left side:
[tex]\[ -2 \cdot (bx) + (-2) \cdot (-5) = -2bx + 10 \][/tex]
2. Substitute and equate it to 16:
[tex]\[ -2bx + 10 = 16 \][/tex]
3. Isolate the term with [tex]\(x\)[/tex] by subtracting 10 from both sides:
[tex]\[ -2bx + 10 - 10 = 16 - 10 \][/tex]
[tex]\[ -2bx = 6 \][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-2b\)[/tex]:
[tex]\[ x = \frac{6}{-2b} \][/tex]
Simplify the fraction:
[tex]\[ x = \frac{6}{-2b} = \frac{6}{-2} \cdot \frac{1}{b} = -3 \cdot \frac{1}{b} = -\frac{3}{b} \][/tex]
Thus, the value of [tex]\(x\)[/tex] in terms of [tex]\(b\)[/tex] is [tex]\(-\frac{3}{b}\)[/tex].
### Solving for [tex]\(x\)[/tex] when [tex]\(b\)[/tex] is 3:
1. Substitute [tex]\(b = 3\)[/tex] into the equation [tex]\( x = -\frac{3}{b} \)[/tex]:
[tex]\[ x = -\frac{3}{3} \][/tex]
2. Simplify:
[tex]\[ x = -1 \][/tex]
Thus, the value of [tex]\(x\)[/tex] when [tex]\(b\)[/tex] is 3 is [tex]\(-1\)[/tex].
So, the final answers are:
- The value of [tex]\(x\)[/tex] in terms of [tex]\(b\)[/tex] is [tex]\(-\frac{3}{b}\)[/tex]
- The value of [tex]\(x\)[/tex] when [tex]\(b\)[/tex] is 3 is [tex]\(-1\)[/tex]
