Question

escribe ways in which solving a linear inequality is similar to solving a linear equation.Choose the correct answer below.A. They are similar in that both involve multiplying or dividing both sides by the coefficient of x to isolate x, regardless of the sign of the coefficientkeeping everything else the same.OB. They are similar in that the equation or inequality can be rewritten by exchanging the left and right sides, or by setting one side equal to 0 andvariable on the other side.OC. They are similar in that a value can be added or subtracted from both sides without changing the solution to the inequality or equation.OD. They are similar in that both involve multiplying or dividing both sides by the reciprocal of the coefficient of x to isolate x, regardless of the signcoefficient, while keeping everything else the same.

Answer 1

Notice that, in the case of an inequality,

`\begin{gathered} x\ge y \\ \Rightarrow x+c\ge y+c,\text{ regardless of the sign of c} \\ \Rightarrow ax\ge ay,\text{ if a}>0 \\ \Rightarrow bx\leq by,\text{ if b}<0 \end{gathered}`

And it is not true that,

`a\ge b\Rightarrow b\ge a!!!`

Therefore, the answer is option C, since addition and subtraction are the only operations that do not modify the result of an inequality.