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Write the phrase as an algebraic expression and simplify if possible. Let [tex]$x$[/tex] represent the unknown number.

"The sum of 5, four times a number, -7, and five times a number."

Sagot :

GinnyAnswer
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]
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