Home > Algebra > Multi-Step Inequalities

How do you solve and write the following in interval notation: #9< -2x+3<=17#?

Answer 1

Ethan Adkins

Solution : # -7 <= x < -3 # , in interval notation: #[-7,-3)#

# 9 < -2x +3 <= 17 or 9-3 < -2x +3-3 <= 17 -3 # or

#6 < -2x <= 14 or 3 < -x <= 7 or -3 > x >= -7# or

# -7 <= x < -3 # , x lies between # [-7 and -3) #.

Note: When mutiplied or divided by negative quantity the inequality

sign reverses.

Solution : # -7 <= x < -3 # , in interval notation #[-7,-3)# [Ans]

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

Answer 2

Isaiah Anthony

To solve and write the inequality ( 9 < -2x + 3 \leq 17 ) in interval notation, follow these steps:

Subtract 3 from all parts of the inequality to isolate the variable.
Divide all parts by -2 to solve for x.
Write the solution in interval notation.

Step 1: ( 9 - 3 < -2x + 3 - 3 \leq 17 - 3 ) ( 6 < -2x \leq 14 )

Step 2: ( \frac{6}{-2} > \frac{-2x}{-2} \geq \frac{14}{-2} ) ( -3 > x \geq -7 )

Step 3: ( x ) belongs to the interval ( [-7, -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 and write the following in interval notation: #9&lt; -2x+3&lt;=17#?

How do you solve and write the following in interval notation: #9< -2x+3<=17#?