Let's break down the given phrase step-by-step and translate it into an algebraic expression.
1. Identify each part of the phrase:
- "The sum of" indicates that we will be adding several terms together.
- "5" is a constant term.
- "Four times a number" can be represented as [tex]\( 4x \)[/tex], where [tex]\( x \)[/tex] is the unknown number.
- "-7" is a constant term.
- "Five times a number" can be represented as [tex]\( 5x \)[/tex].
2. Write the algebraic expression:
- We need to add all the identified terms together. Therefore, we can write the algebraic expression as:
[tex]\[
5 + 4x - 7 + 5x
\][/tex]
3. Simplify the expression:
- Combine the constant terms [tex]\( 5 \)[/tex] and [tex]\( -7 \)[/tex]:
[tex]\[
5 - 7 = -2
\][/tex]
- Combine the terms that contain [tex]\( x \)[/tex], which are [tex]\( 4x \)[/tex] and [tex]\( 5x \)[/tex]:
[tex]\[
4x + 5x = 9x
\][/tex]
4. Write the simplified expression:
- Putting it all together, we have:
[tex]\[
9x - 2
\][/tex]
Therefore, the simplified algebraic expression is:
[tex]\[
9x - 2
\][/tex]
