Question

How do you solve \[y - 3 < 5y + 1\]?

Answer 1

Hint: An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. Here we need to solve for ‘y’ which is a variable. Solving the given inequality is very like solving equations and we do most of the same thing but we must pay attention to the direction of inequality\[( \leqslant , > )\]. We have a simple linear equation type inequality and we can solve this easily.

Complete step by step answer:
Given \[y - 3 < 5y + 1\]
We need to solve for ‘y’.
Since we know that the direction of inequality doesn’t change if we add a number on both sides. We add 3 on both sides of the inequality we have,
\[y < 5y + 1 + 3\]
Also we know that the direction of inequality doesn’t change if we subtract a number on both sides. We subtract 5y on both sides of the inequality we have,
\[y - 5y < + 1 + 3\]
\[ - 4y < 4\]
We divide the whole equation by -4 and the direction changes we have,
\[ \Rightarrow y > - 1\]

That is \[y > - 1\] is the solution of \[y - 3 < 5y + 1\].

Note: We know that \[a \ne b\] it says that ‘a’ is not equal to ‘b’. \[a > b\] means that ‘a’ is less than ‘b’. \[a < b\] means that ‘a’ is greater than ‘b’. These two are known as strict inequality. \[a \geqslant b\] means that ‘a’ is less than or equal to ‘b’. \[a \leqslant b\] means that ‘a’ is greater than or equal to ‘b’.
The direction of inequality do not change in these cases:
\[ \bullet \]Add or subtract a number from both sides.
\[ \bullet \]Multiply or divide both sides by a positive number.
\[ \bullet \]Simplify a side.
The direction of the inequality change in these cases:
\[ \bullet \]Multiply or divide both sides by a negative number.
\[ \bullet \]Swapping left and right hand sides.