Question

How do you solve the inequality \[ - 2x + 3 > 7\] ?

Answer 1

Hint:Here in this question we have solved the given inequality. We have arithmetic operations, by using this or by shifting the numbers in the equality we are going to find the value of x. and hence we obtain the value of x such that the value of x should satisfy the above inequality.

Complete step by step answer:
In mathematics we have for different kinds of arithmetic operations. They are,
-Addition (+) which adds the numbers.
-Subtraction (-) which subtracts the numbers.
-Multiplication (\[ \times \]) which multiply the numbers.
-Division (\[ \div \]) which divides the numbers.
Now consider the inequality \[ - 2x + 3 > 7\]. To above inequality subtract 3 on the both sides. We have
\[ \Rightarrow - 2x + 3 - 3 > 7 - 3\]
In the LHS of the above inequality the -3 and +3 will cancel. In the RHS of the above inequation we are subtracting the number 3 from 7, we have
\[ \Rightarrow - 2x > 4\]
Multiply the above inequality by -1 we get
\[ \Rightarrow 2x < - 4\]
Divide the above inequality by 2 we have
\[ \Rightarrow x < - 2\]
We can also solve this inequality by shifting the number either from LHS to RHS or from RHS to LHS.
Now consider the inequality \[ - 2x + 3 > 7\]
When we shift the number +3 to RHS it will become -3. So we have
\[- 2x > 7 - 3 \\
\Rightarrow - 2x > 4 \\ \]
Multiply the above inequality by -1 we get
\[ \Rightarrow 2x < - 4\]
Divide the above inequality by 2 we have
\[ \therefore x < - 2\]
Hence, we have solved the above inequality. And we got the solution. Here the value of x must be less than -2 and it should not exceed. The maximum number the variable x takes is -1. The variable should not exceed the negative value (-1).

Note:The arithmetic symbols, < is less than symbol, > is the greater than symbol and = is the equal to symbol. Suppose if the inequality involves \[x < a\], this tells that the value of x should not exceed than the number a. if the inequality involves \[x > a\], this tells that the value of x should take the number greater than the number a. if the inequality involves \[x = a\], this tells that the value of x should be equal to the number a.