Question

How do you solve the equation $7-\dfrac{2}{3}x < x-8$ ?

Answer 1

To solve the given inequality we will first multiply the equation by the denominator of fraction to make all the coefficient and constants integers. Now we will bring all the variable terms and constant terms on opposite sides and hence solve the equation by simplifying it further.

Complete step-by-step solution:
Now consider the given inequality $7-\dfrac{2}{3}x< x-8$.
To solve the inequality we will first multiply the whole equation by 3 to make all the coefficient and constants integer.
Hence we get $21 – 2x < 3x – 24$
Now we will transpose the term 2x on RHS. Hence we get,$21 < 3x – 24 + 2x$
Now similarly we will transpose the term 24 on LHS. Hence we get $21 + 24 < 3x + 2x.$
Now since we have all the variable terms on one side of equation and the constant on other side we can simplify the equation
Hence simplifying the equation we get $45 < 5x.$
Now let us divide the whole equation by 5. Hence we get, $9 < x.$
**Hence the solution of the given equation is $x < 9$. **

Note: Note that if there are two or more fractions in the equation first we will multiply the equation by LCM of denominators of fractions. Then we will further solve it by simplifying the equation. Also note that the sign of inequality changes when the equation is multiplied or divided by a negative number.