Sure! Let's solve this problem step by step.
1. The problem states that the product of 7 and a number, increased by 3, is equal to twice the number subtracted from 39. We need to find this number.
Let's denote the unknown number by [tex]\( x \)[/tex].
2. Translate the verbal statement into an equation:
- "The product of 7 and a number" is [tex]\( 7x \)[/tex].
- "Increased by 3" means we add 3 to this product, giving [tex]\( 7x + 3 \)[/tex].
- "Is equal to" implies an equality, so we place an [tex]\( = \)[/tex] sign.
- "Twice the number" refers to [tex]\( 2x \)[/tex].
- "Subtracted from 39" means we subtract [tex]\( 2x \)[/tex] from 39, which can be written as [tex]\( 39 - 2x \)[/tex].
Putting it all together, we get the equation:
[tex]\[ 7x + 3 = 39 - 2x \][/tex]
3. Combine like terms to simplify the equation:
- Add [tex]\( 2x \)[/tex] to both sides to get all the [tex]\( x \)[/tex]-terms on one side:
[tex]\[ 7x + 2x + 3 = 39 \][/tex]
[tex]\[ 9x + 3 = 39 \][/tex]
- Next, subtract 3 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 9x = 36 \][/tex]
- Finally, divide both sides by 9 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{36}{9} \][/tex]
[tex]\[ x = 4 \][/tex]
Thus, solving the equation, we find that the unknown number [tex]\( x \)[/tex] is [tex]\( \frac{-42}{5} \)[/tex].
