Question

How do you solve the inequality \[2x+7\le 19\] ?

Answer 1

Hint: Now the given inequality is a linear inequality in one variable. To solve the inequality we will first separate the variable and the constant terms and simplify. Then we will divide the whole equation by the coefficient of x and hence find the solution of the equation.

Complete step by step solution:
Now we are given a linear inequality in one variable in the form of ax + b < c.
To solve the equation we want to find the set of all values of x such that the values satisfy the given inequality.
Now to solve the given inequality we will first separate the variables and constants.
To do so consider the given inequality \[2x+7\le 19\] .
Let us transpose 7 on RHS. Hence we will get the inequality as,
$\Rightarrow 2x\le 19-7$
Now we have separated the constant and variables, hence we will simplify the equation.
$\Rightarrow 2x\le 12$
Now we want to find the value of x hence we will divide the whole equation by coefficient of x. here we have the coefficient of x is 2. Hence on division we get,
$\begin{align}
  & \Rightarrow x\le \dfrac{12}{6} \\
 & \Rightarrow x\le 6 \\
\end{align}$
Hence we have the solution of the given inequality is $x\le 6$ which means all the real numbers less than or equal to 6.
Hence we get the solution set as $\left( -\infty ,6 \right]$ .

Note: Now note that while transposing terms from one side to another side the sign of those terms changes. Hence positive terms become negative and negative terms become positive. Also note that in the solution set 6 is included hence we put a square bracket and not an open bracket towards 6.