How do you solve the inequality #-c -19#?

Question

How do you solve the inequality #-c > -19#?

Levi Adams · Accepted Answer

#c<19#

Consider the following True statement.

#-4 > -7larrcolor(blue)"TRUE"#

If we now multiply both sides of the inequality by - 1

#(-1xx-4)>(-1xx-7)#

We obtain.

#4 > 7larrcolor(red)" FALSE"#

To make the statement True, we must reverse the sign.

That is #4<7larrcolor(blue)"TRUE"#

Conclusion.

When we multiply or divide an inequality by a #color(magenta)"negative quantity"# we must #color(green)"reverse the sign of the inequality."#

#"for" -c > -19#

multiply both sides by - 1

#(-1xx-c)<(-1xx-19)larrcolor(green)" reverse sign"#

#rArrc<19" is the solution"#

Emery Allen · Answer

#c < 19#

Given:#" "color(red)(-c > -19)#

#color(blue)("Using first principles method")#

Add #c# to both sides

#-c+c> -19+c#

#0> -19+c#

Add 19 to both sides

#0+19 > -19+19+c#

#19 > 0+c#

#19 > c larr#Observe that the 'point' of the sign is towards #c#

So #" "color(red)(c<19)#

Notice that inequality sign is now the other way round

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Using short cut method")#

Multiply both sides by (-1) and reverse the inequality sign.

#(-1)xx(-c)" " <" " (-1)xx(-19)#

#c < 19#

#color(red)("Whenever you multiply by -1 (both sides) reverse the inequality sign")#

Roman Alvarez · Answer

undefined To solve the inequality -c > -19, you need to multiply both sides of the inequality by -1 to make the coefficient of c positive. This reverses the direction of the inequality sign. So, when you multiply both sides by -1, you get c < 19. Therefore, the solution to the inequality is c < 19.

How do you solve the inequality #-c &gt; -19#?

How do you solve the inequality #-c > -19#?