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Solve \[5x - 3 < 7\], when x is an integer

Last updated date: 14th Jun 2024
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Hint: Inequations can be similarly solved in the way we solve equations. Here only the signs “<”,”>” and “≤,≥” are used in the place of “=”. Begin with writing the inequation, remember to follow the rules while taking the numbers to the either sides. Solve for x. Know what are integers and then get the value of x after solving the inequation.

Complete step-by-step solution:
The given inequation can be directly solved as follows;
\[5x - 3 < 7\](bring the like terms together therefore take -3 to the other side of the inequation; )
 \[5x < 7 + 3\] (Add the number here);
\[5x < 10\](Now take “5” to the other side of the inequation; solve for x);
\[x < \dfrac{{10}}{5}\]
\[x < 2\]
Therefore the value of x is any number or integer less than \[2\].
Hence the numbers can be \[\left( {............. - 2, - 1,0,1} \right);\] Here the integer continues below \[ - 2\] as the limit till where to take the numbers has not been given.

Note: While bringing the like terms together; remember that the signs of the number changes while taking them to the other side of the equation. In this question while taking \[ - 3\] to the other side of the equation; the sign changes to \[ + 3\]. When two numbers are in multiplication and if the numbers are taken to the other side of the inequation; then the number is divided by the number on the other side of the inequation. Here \[5\] was in multiplication with “x” ; on going to the other side it became a dividend \[\dfrac{{10}}{5}\].