Question

How do you solve the equation $\dfrac{2x-4}{6}\ge -5x+2$ ?

Answer 1

Hint: Now we are given with a linear equation in one variable. To solve the equation we will first eliminate the fraction by multiplying 6 to the whole equation. Now we will use distributive property to expand the brackets and simplify the equation further to write it in the form of $ax\ge b$ Now we will divide the equation with coefficient of x to find the required condition on x. Hence we have the solution of the given equation.

Complete step by step solution:
Now we are given with a linear equation in x.
Now consider the given equation $\dfrac{2x-4}{6}\ge -5x+2$ .
To solve the equation we will first try to eliminate the fraction.
Hence we will multiply the whole equation by 6.
$\Rightarrow \left( 2x-4 \right)\ge 6\left( -5x+2 \right)$
Now we know according to distributive property that $a\left( b+c \right)=ab+ac$ hence we get the above equation as,
$\Rightarrow 2x-4\ge 6\left( -5x \right)+6\left( 2 \right)$
Now on simplifying the above equation we get,
$\Rightarrow 2x-4\ge -30x+12$
Now we will shift all the terms with x from RHS to LHS and all the constants from LHS to RHS. Hence we will simplify the equation and write it in the form of $ax=b$ .
$\begin{align}
  & \Rightarrow 2x+30x\ge 12+4 \\
 & \Rightarrow 32x\ge 16 \\
\end{align}$
Now dividing the whole equation by 32 we get,
$\begin{align}
  & \Rightarrow x\ge \dfrac{16}{32} \\
 & \Rightarrow x\ge \dfrac{1}{2} \\
\end{align}$
Hence the solution of the given equation is $\left( \dfrac{1}{2},\infty \right)$

Note: Now note that since we have an inequality we will get a range of solutions and not a particular solution. Now we can always check the solution by substituting the values of x in the equation. Hence for all x in the solution interval must satisfy the equation and all x which are not from the obtained interval must not satisfy the given equation.