Video Transcript
Solve the inequality 19 plus seven 𝑥 is less than 40 for all rational numbers.
The 𝑄 symbol in the question means all the rational numbers. A rational number is any number that can be written as a fraction 𝑎 over 𝑏, where 𝑎 and 𝑏 are integers. We can solve the inequality in this question, 19 plus seven 𝑥 is less than 40, using the balancing method and inverse operations. The opposite or inverse of adding 19 is subtracting 19. So we begin by doing this to both sides of the inequality. 40 minus 19 is equal to 21. Therefore, seven 𝑥 is less than 21.
Our next step is to divide both sides of this line by seven. Seven 𝑥 divided by seven is 𝑥 and 21 divided by seven is three. The solution to our inequality is 𝑥 is less than three. This answer can be written using set notation such that 𝑥 is the set of all rational numbers that are less than three.
