Certainly! Let's tackle each part of the problem step-by-step.
### Example 1: Writing Algebraic Expressions from Verbal Expressions
22. The difference between the product of four and a number and five.
First, identify the key parts of the verbal expression:
- "product of four and a number" can be written as [tex]\( 4x \)[/tex] where [tex]\( x \)[/tex] is the number.
- "difference between" suggests a subtraction.
- The expression "and five" means we subtract five from the product.
Thus, the algebraic expression is:
[tex]\[ 4x - 5 \][/tex]
23. The product of the square of a number and 8.
- "the square of a number" can be written as [tex]\( x^2 \)[/tex].
- "product ... and 8" suggests multiplication.
Thus, the algebraic expression is:
[tex]\[ 8x^2 \][/tex]
24. Fifteen less than the cube of a number.
- "the cube of a number" is [tex]\( x^3 \)[/tex].
- "fifteen less than" suggests we subtract fifteen from the cube.
Thus, the algebraic expression is:
[tex]\[ x^3 - 15 \][/tex]
25. Five more than the quotient of a number and 4.
- "the quotient of a number and 4" is written as [tex]\( \frac{x}{4} \)[/tex].
- "five more than" suggests we add five.
Thus, the algebraic expression is:
[tex]\[ \frac{x}{4} + 5 \][/tex]
### Example 2: Writing Verbal Sentences from Equations
26. [tex]\( 8x - 4 = 16 \)[/tex]
First, break down the equation to create a verbal sentence:
- [tex]\( 8x \)[/tex] represents "eight times a number."
- Subtracting 4 can be described as "four less than eight times a number."
- The equation equals 16.
Putting it together, the verbal sentence is:
"Four less than eight times a number is sixteen."
27. [tex]\( \frac{x + 3}{4} = 5 \)[/tex]
- [tex]\( x + 3 \)[/tex] represents "three more than a number."
- The fraction [tex]\( \frac{x + 3}{4} \)[/tex] can be expressed as "the quotient of three more than a number and 4."
- The equation equals 5.
So, the verbal sentence is:
"The quotient of three more than a number and 4 is equal to five."
I hope this detailed breakdown helps you understand how to convert verbal expressions to algebraic expressions and vice versa!
