Home > Algebra > Multi-Step Inequalities

How do you solve #-12<8-x<=-7 #?

Answer 1

Savannah Anderson

#15<=x<20#

#-12<8-x# so #x<20#

the other hand

#8-x<=-7# so #x>=15#

combine these two results #15<=x<20#

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

Answer 2

Jace Anderson

To solve the inequality ( -12 < 8 - x \leq -7 ), you can start by isolating ( x ) by performing operations to both sides of the inequality.

Subtract 8 from all parts of the inequality: [ -12 - 8 < 8 - x - 8 \leq -7 - 8 ] [ -20 < -x \leq -15 ]
To get rid of the negative sign in front of ( x ), you need to multiply all parts of the inequality by -1. When you multiply or divide by a negative number, you must reverse the inequality signs. [ -1(-20) > -1(-x) \geq -1(-15) ] [ 20 > x \geq 15 ]

So, the solution to the inequality is ( 15 \leq x < 20 ).

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 #-12&lt;8-x&lt;=-7 #?

How do you solve #-12<8-x<=-7 #?