Question

How do you solve \[5-2x<7\]?

Answer 1

Hint: This is a linear inequality equation in one variable as there is only one variable in an equation. In the given question, the variable is the letter ‘\[x\]’, to solve this question we need to get ‘\[x\]’ on one side of the “equals” sign, and all the other numbers on the other side. Solving linear inequality is the same as solving the general equation but there is one more rule i.e. changing the sign of inequality if we multiply both sides by a negative number. To solve this inequality for a given variable ‘\[x\]’, we have to undo the mathematical operations such as addition, subtraction, multiplication and division that have been done to the variables. In this way we will get our required answer.

Complete step by step solution:
We have the given equation;
\[\Rightarrow 5-2x<7\]
subtracting 5 to both the sides of the inequality, we obtain
\[\Rightarrow 5-2x-5<7-5\]
Simplifying the numbers in the above inequality, we get
\[\Rightarrow -2x<2\]
Dividing both the sides of inequality by 2, we get
\[\Rightarrow \dfrac{-2x}{2}<\dfrac{2}{2}\]
Simplifying the numbers in the above inequality, we get
\[\Rightarrow -x<1\]
Multiply both the sides of the inequality by -1, we obtain
\[\Rightarrow -x\times -1>1\times -1\]
In the above inequality, the sign of inequality changes as we multiply both the sides by a negative number.
Therefore, we get
\[\Rightarrow x>-1\]
Therefore, all the numbers which are greater than -1 are the possible values of ‘x’.
It is the required solution.

Note: Use addition or subtraction properties of inequality to gather variable terms on one side of the inequality and constant on the other side of the equation. The important thing to recollect about any inequality is that the ‘equals’ sign represents a balance. Use the multiplication or division properties of equality to form the coefficient of the variable term equivalent to 1.in solving inequality there is one sign changing rule i.e. sign of the inequality will be changed if we multiply both the sides of the equation by negative number. This is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.