Sure, let's break down the description step-by-step to match it with the given inequality:
[tex]\[5(x + 3) \geq \frac{x}{-7}\][/tex]
1. Five times the sum of a number, [tex]\( x \)[/tex], and three:
- The phrase "sum of a number, [tex]\( x \)[/tex], and three" can be written as [tex]\( x + 3 \)[/tex].
- Multiplying this sum by five, we get [tex]\( 5(x + 3) \)[/tex].
2. The phrase "is at least equal to":
- This phrase indicates a comparison where one side is at least as large as the other. Mathematically, this is represented by the "greater than or equal to" symbol, [tex]\( \geq \)[/tex].
3. The quotient of [tex]\( x \)[/tex] and negative seven:
- The quotient of [tex]\( x \)[/tex] and negative seven can be written as [tex]\( \frac{x}{-7} \)[/tex].
Putting it all together, we have:
[tex]\[5(x + 3) \geq \frac{x}{-7}\][/tex]
Let's verify:
- The description "five times the sum of a number, [tex]\( x \)[/tex], and three" translates to [tex]\( 5(x + 3) \)[/tex].
- The phrase "is at least equal to" uses the [tex]\( \geq \)[/tex] symbol.
- The phrase "the quotient of [tex]\( x \)[/tex] and negative seven" translates to [tex]\( \frac{x}{-7} \)[/tex].
So, the inequality representation:
[tex]\[5(x + 3) \geq \frac{x}{-7}\][/tex]
Thus, Kendra is correct. The given description can indeed be represented by the inequality [tex]\( 5(x + 3) \geq \frac{x}{-7} \)[/tex].
