Home > Algebra > Multi-Step Inequalities

How do you solve #2-3(x+2)<11#?

Answer 1

#x > -5#

Treat inequalities in the same way as an equation, unless you multiply or divide by a negative number, in which case the inequality sign will change around.

#2-3(x+2)<11" remove brackets"#

#2-3x-6 <11" the x-term is negative"#

Either:#color(white)(.........................................)# Or

#color(red)(-4-11 <3x) color(white)(................................)color(blue)(-3x <11-2+6)#

#color(red)(-15 <3x)" "div 3color(white)(...................)color(blue)(-3x < 15)#

#color(red)(-5 < x)color(white)(.............................................) color(blue)((-3x)/(-3)>15/(-3))" "div -3#

#color(red)(rArr x > -5)color(white)(.........................................) color(blue)(x> -5)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Isaiah Anthony

To solve 2 - 3(x + 2) < 11, first distribute the -3 across the expression inside the parentheses, then combine like terms, and isolate the variable x by performing the necessary operations.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #2-3(x+2)&lt;11#?

How do you solve #2-3(x+2)<11#?