Question

How do you solve \[-2x+4<12\]?

Answer 1

Hint: Now we are given with the inequality in x. to solve the inequality we will first separate the variable and constants. Now we will simplify the inequality and divide by the coefficient of x to find the value of x. Hence we have the condition of x from which we can write the solution of the given equation.

Complete step by step solution:
Now we are given with a linear inequality in x.
Now consider the given equation $-2x+4<12$
To solve the inequality we will rearrange the terms of the equation by separating the variables and constants.
Now to do so let us subtract 4 on both sides. Hence we get,
$\Rightarrow -2x+4-4 < 12-4$
Now on simplifying the above equation we get,
$\Rightarrow -2x < 8$
Now on multiplying the whole equation by – 1 we get,
$\Rightarrow 2x > 8$
Now we have the equation in the form of $ax>b$ to solve the equation we divide the equation by the coefficient of x which is a.
Hence on dividing the whole inequality by 2 we get,
$\Rightarrow x>4$
Hence all values of x greater than 4 will satisfy this inequality
Hence the solution of the given equation is $\left( 4,\infty \right)$ .

Note: Now note that solving inequality is almost the same as solving inequality. We perform the same algebraic operations in both the cases but remember if we multiply the inequality by a negative number the sign changes. Similarly if we divide the equation by a negative number the sign changes. Hence $ < $ becomes $>$ and vice versa. Now also note that in linear inequalities we do not get a particular solution but a set of solutions.