Home > Algebra > Compound Inequalities

How do you solve #7>1-2x<=10#?

Answer 1

Eli Assouline

Split the compound inequality into 2 simple inequalities; simplify each; re-combine

#7>1-2x<=10#

Inequality Part 1: #7>1-2x# #rarr 2x > -6# #rarr x> -3#

Inequality Part 2: #1-2x<=10# #rarr -9 <= 2x# #rarr x>= -9/2#

Recombining: #x> -3# and #x>=-9/2# simplifies to #x > -3# (since if #x> -3 rarr x>= -9/2#)

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

Answer 2

Kennedy Adams

To solve (7 > 1 - 2x \leq 10), you need to solve each inequality separately and then find the intersection of the solutions.

First, solve (1 - 2x \leq 10):

[ 1 - 2x \leq 10 \implies -2x \leq 9 \implies x \geq -\frac{9}{2} ]

Next, solve (7 > 1 - 2x):

[ 7 > 1 - 2x \implies 6 > -2x \implies -3 < x ]

Combining the solutions, we have:

[ -\frac{9}{2} \leq x < -3 ]

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 #7&gt;1-2x&lt;=10#?

How do you solve #7>1-2x<=10#?