Question

How do you solve the inequality\[38 < 4x + 3 + 7 - 3x\]?

Answer 1

Hint:For any inequality when you are solving you should know the sign of inequality changes when you multiply minus sign both the side, and rest solution can be done same as that for equals sign is done, nor any other assumption should be needed.

Complete step by step solution:
In the given equation \[38 < 4x + 3 + 7 - 3x\]

In the right side of inequality there can be certain simplification, and after simplifying we can direct
solve it:
\[
38 < 4x + (3 + 7) - 3x \\
38 < (4x - 3x) + 10 \\
38 < 10x - 10 \\
38 + 10 < 10x \\
48 < 10x \\
x > 4.8 \\
\]

Here we get the range of \[x\]that is it is greater than\[4.8\], which implies that the given quantity can have any possible value above \[4.8\]

Range of \[x\]can be written as\[(4.8,\infty )\], here open bracket “\[()\]” is indicating that the value written in the bracket is not for the quantity \[x\]but the very next closed value after \[4.8\]is the value of \[x\], and since infinity is not known so we always provide an open bracket for infinity.

Additional Information: If you are given the equals to sign with inequalities then also the process would be the same the only change would be in describing the range of the quantity, that is closed bracket would be used instead of an open bracket.

Note: Inequality basically defines the region of the quantity whosoever for which the inequality is used for, that is it gives you a range of possible values for the quantity you are finding for. In this range real as also complex range also occurs.