-5<= 4-9x<-2 — step-by-step solution

1) We have the following 2 conditions:

[1]:

-5 \leq 4 - 9 x

[2]:

4 - 9 x < -2

2) Solving for x:

-5 \leq 4 - 9 x

[1]

4 - 9 x \geq -5

ⓘ We gather the terms in

x

on the right and the other terms on the left

4 + 5 \geq 9 x

ⓘ Start from

4

and move forward

5

on the number line:

4 + 5

9

9 \geq 9 x

ⓘ Both sides are divided by

9

x \leq \frac{9}{9}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

9

, their greatest common divisor:

\frac{9}{9}

1

Solution obtained [1]:

x \leq 1

3) Solving for x:

4 - 9 x < -2

[2] where

x \leq 1

4 - 9 x < -2

ⓘ We gather the terms in

x

on the right and the other terms on the left

4 + 2 < 9 x

ⓘ Start from

4

and move forward

2

on the number line:

4 + 2

6

6 < 9 x

ⓘ Both sides are divided by

9

x > \frac{6}{9}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{6}{9}

\frac{2 \cdot 3}{3 \cdot 3}

\frac{2}{3}

Solution obtained [2]:

x > \frac{2}{3}

Intersecting

x \leq 1

and

x > \frac{2}{3}

gives

x \in (\frac{2}{3}, 1]

▶Solution:

x \in (\frac{2}{3}, 1]

4) The numeric value of:

x \in (\frac{2}{3}, 1]

equals:

▷

x \in (\approx 0.6667, 1]