What is the inequality that describes the relationship when 3 is added to the product of 7 and a number x, and this sum is less than 26?

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To express the situation described in your question, we first need to break down the components of the inequality.

We are given that:

  • The product of 7 and a variable x is 7x.
  • We then add 3 to this product, leading to 7x + 3.
  • This sum is stated to be less than 26.

Putting all of this together, we can write the inequality as:

7x + 3 < 26

Next, we can solve for x to find the range of values that satisfy this inequality:

1. Start by subtracting 3 from both sides:

7x < 26 - 3
7x < 23

2. Now, divide both sides by 7:

x < &frac23

Thus, the solution to the inequality 7x + 3 < 26 is:

x < &frac{23}{7}

or approximately x < 3.29.

In conclusion, if you add 3 to the product of 7 and a number x, that result must be less than 26 when x is less than 3.29.

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