8x+2>348x+2>34 — step-by-step solution

1) We have the following 2 conditions:

[1]:

8 x + 2 > 348 x + 2

[2]:

348 x + 2 > 34

2) Solving for x:

8 x + 2 > 348 x + 2

[1]

8 x

+ 2

- 348 x

- 2 > 0

ⓘ Start from

2

and move back

2

on the number line, down to zero:

2 - 2

0

■Like terms are grouped by adding their coefficients:

8 x - 348 x

-340 x

- 340 x + 0 > 0

ⓘ Adding 0 changes nothing:

- 340 x + 0

-340 x

- 340 x > 0

We simplify the expression by

-340

and since

-340

is negative, we reverse the inequality sign

⇥Solution obtained [1]:

x < 0

3) Let's solve for x:

348 x + 2 > 34

[2] where

x < 0

348 x + 2 > 34

ⓘ We subtract

2

from both sides

348 x > 34 - 2

ⓘ Start from

34

and move back

2

on the number line:

34 - 2

32

348 x > 32

ⓘ Both sides are divided by

348

x > \frac{32}{348}

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

4

, their greatest common divisor:

\frac{32}{348}

\frac{8 \cdot 4}{87 \cdot 4}

\frac{8}{87}

Solution found [2]:

x > \frac{8}{87}

No value of

x

satisfies both

x < 0

and

x > \frac{8}{87}

▶Solution:

\emptyset