2x+8>= 8(x-5)>7(x+3)-x — step-by-step solution

1) We have the following 2 conditions:

[1]:

2 x + 8 \geq 8 \cdot (x - 5)

[2]:

8 \cdot (x - 5) > 7 \cdot (x + 3) - x

2) Let's solve for x:

2 x + 8 \geq 8 \cdot (x - 5)

[1]

2 x + 8 \geq 8 \cdot (x - 5)

2 x + 8 \geq 8 x - 40

8 + 40 \geq 8 x - 2 x

ℹ

8 + 40

48

‖

8 x - 2 x

6 x

48 \geq 6 x

x \leq \frac{48}{6}

Solution obtained [1]:

x \leq 8

3) Solving for x:

8 \cdot (x - 5) > 7 \cdot (x + 3) - x

[2] where

x \leq 8

8 \cdot (x - 5) > 7 \cdot (x + 3) - x

ℹ

8 \cdot (x - 5)

8 x - 40

‖

7 \cdot (x + 3)

7 x + 21

8 x - 40 > (7 x + 21) - x

8 x - 40 > 6 x + 21

8 x > 6 x + 61

8 x - 6 x > 61

2 x > 61

Solution obtained [2]:

x > \frac{61}{2}

Let's build the table of the different terms to determine the global solution:

No solution in

ℝ

for:

x

▶Solution:

\emptyset