Question

How do you solve \[7x + 8 > 22\]?

Answer 1

Hint: Here in this question, we have to solve the given inequality to the x variable. The given equation is the algebraic inequality with one variable x, this can be solve by add or subtract the necessary term from each side of the inequality to isolate the term with the variable x, then multiply or divide each side of the inequality by the appropriate value, while keeping the inequality balanced then solve the resultant balance inequality for the x value.

Complete step-by-step solution:
An inequality is like an equation, except instead of saying that the two values are equal, an inequality shows a “greater than” or “less than” relationship. The \[ > \] sign means “greater than.” The \[ < \] means “less than.”
 Consider the given inequality
\[7x + 8 > 22\]--------(1)
Where x is the variable, it having the greater than inequality
Now, we have to solve the above inequality for the variable x
Subtract 8 on both side in equation (1), then
\[ \Rightarrow \,\,\,7x + 8 - 8 > 22 - 8\]
On simplification, we get
\[ \Rightarrow \,\,\,7x > 14\]--------(2)
To isolate the x variable, Divide 7 on both side
\[ \Rightarrow \,\,\,\dfrac{7}{7}x > \dfrac{{14}}{7}\]
\[ \Rightarrow \,\,\,x > 2\]
Or it can also be written in the form of interval as \[\left( {2,\infty } \right)\]

Hence, the required solution is \[\,x > 2\].

Note: If the algebraic expression contains only one unknown, we determine the value by using simple multiplication and division. . The tables of multiplication should be known to solve these kinds of problems. since we have greater than inequality we can’t say the exact value of x. While shifting the terms we must be aware of the sign of a term.