Sure, let's solve each part step by step:
### Given the function: [tex]\( n(x) = 7x + 4 \)[/tex]
#### Part (a): Find [tex]\( x \)[/tex] when [tex]\( n(x) = 39 \)[/tex]
1. Start with the equation:
[tex]\[ 7x + 4 = 39 \][/tex]
2. Subtract 4 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 7x = 39 - 4 \][/tex]
3. Simplify the right-hand side:
[tex]\[ 7x = 35 \][/tex]
4. Divide both sides by 7 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{35}{7} \][/tex]
5. Simplify the fraction:
[tex]\[ x = 5 \][/tex]
So, [tex]\( x = 5 \)[/tex] when [tex]\( n(x) = 39 \)[/tex].
#### Part (b): Find [tex]\( x \)[/tex] when [tex]\( n(x) = 0 \)[/tex]
1. Start with the equation:
[tex]\[ 7x + 4 = 0 \][/tex]
2. Subtract 4 from both sides:
[tex]\[ 7x = 0 - 4 \][/tex]
3. Simplify the right-hand side:
[tex]\[ 7x = -4 \][/tex]
4. Divide both sides by 7 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-4}{7} \][/tex]
5. Simplify the fraction:
[tex]\[ x = -0.5714285714285714 \][/tex]
So, [tex]\( x = -0.5714285714285714 \)[/tex] when [tex]\( n(x) = 0 \)[/tex].
#### Part (c): Find [tex]\( x \)[/tex] when [tex]\( n(x) = 4 \)[/tex]
1. Start with the equation:
[tex]\[ 7x + 4 = 4 \][/tex]
2. Subtract 4 from both sides:
[tex]\[ 7x = 4 - 4 \][/tex]
3. Simplify the right-hand side:
[tex]\[ 7x = 0 \][/tex]
4. Divide both sides by 7:
[tex]\[ x = \frac{0}{7} \][/tex]
5. Simplify the expression:
[tex]\[ x = 0 \][/tex]
So, [tex]\( x = 0 \)[/tex] when [tex]\( n(x) = 4 \)[/tex].
#### Part (d): Find [tex]\( x \)[/tex] when [tex]\( n(x) = 13 \)[/tex]
1. Start with the equation:
[tex]\[ 7x + 4 = 13 \][/tex]
2. Subtract 4 from both sides:
[tex]\[ 7x = 13 - 4 \][/tex]
3. Simplify the right-hand side:
[tex]\[ 7x = 9 \][/tex]
4. Divide both sides by 7:
[tex]\[ x = \frac{9}{7} \][/tex]
5. Simplify the fraction:
[tex]\[ x = 1.2857142857142858 \][/tex]
So, [tex]\( x = 1.2857142857142858 \)[/tex] when [tex]\( n(x) = 13 \)[/tex].
### Summary:
- [tex]\( x = 5 \)[/tex] when [tex]\( n(x) = 39 \)[/tex].
- [tex]\( x = -0.5714285714285714 \)[/tex] when [tex]\( n(x) = 0 \)[/tex].
- [tex]\( x = 0 \)[/tex] when [tex]\( n(x) = 4 \)[/tex].
- [tex]\( x = 1.2857142857142858 \)[/tex] when [tex]\( n(x) = 13 \)[/tex].
