Inequalities with a variable: how a component affects the result
Solve inequalities with a variable in two ways: by selection and by reducing to an equation. Write the answer with an ellipsis. Ukrainian grades 3–4.
- Ukraine: grade 4
- Russia: grade 4
Guide
A studio for Ukrainian grades 3–4 (NUS textbooks: grade 3 part 2 «Meet inequalities with a variable»; grade 4 part 1 «Exploring equations and inequalities with a variable»). To solve an inequality with a variable is to find the values of the variable for which it becomes a true numerical inequality. Such a value is called a solution of the inequality.
Selection method: put the numbers in one by one. If k = 22, then 22 − 8 < 10 is false, so 22 is not a solution. If k = 14, then 14 − 8 < 10 is true, so 14 is a solution.
Reducing to an equation: change 16 − p > 8 into the equation 16 − p = 8, find p = 8 and check the numbers next to it, 7 and 9.
An inequality can also be solved using how the result depends on a change of a component. Of two differences with equal subtrahends the bigger is the one with the bigger minuend. An answer with infinitely many solutions ends with an ellipsis: 13, 14, 15, ...