Sure, let's solve this step-by-step!
1. Let's denote the number Janet picked as [tex]\( x \)[/tex].
2. According to the problem, Janet first added 7 to the number:
[tex]\[
x + 7
\][/tex]
3. Then, she multiplied the result by 2:
[tex]\[
2 \times (x + 7)
\][/tex]
4. Next, she subtracted 4 from the outcome:
[tex]\[
2(x + 7) - 4
\][/tex]
5. We are given that the final result is 28:
[tex]\[
2(x + 7) - 4 = 28
\][/tex]
6. To find [tex]\( x \)[/tex], let's solve this equation step-by-step. First, simplify the expression on the left:
[tex]\[
2(x + 7) - 4 = 28
\][/tex]
Expand the terms inside the parenthesis:
[tex]\[
2x + 14 - 4 = 28
\][/tex]
Combine like terms:
[tex]\[
2x + 10 = 28
\][/tex]
7. Solve for [tex]\( x \)[/tex] by isolating it on one side of the equation. First, subtract 10 from both sides:
[tex]\[
2x = 28 - 10
\][/tex]
[tex]\[
2x = 18
\][/tex]
8. Finally, divide both sides by 2:
[tex]\[
x = \frac{18}{2}
\][/tex]
[tex]\[
x = 9
\][/tex]
So, Janet originally picked the number [tex]\( 9 \)[/tex].
