Name: Solving inequalities: solution walkthrough
Uploaded: 2026-11-13
Duration: 2 min 14 s
Description: Which inequality describes all values of x for which 2x - 5 > 5x + 7? Try it, then watch the animated solution.

Gather the

x

terms on one side: subtract

5x

from both sides. That gives

{-3x} - 5 > 7

.

Add

5

to both sides:

{-3x} > 12

. Adding or subtracting never changes the direction of the sign.

Dividing by a negative reverses the order.

1 < 3

, but make both negative and

{-1} > {-3}

.

So divide both sides by

{-3}

and flip

>

to

<

:

x < {-4}

. Open circle at

{-4}

, shade to the left.

Test a number from each side.

x = {-5}

:

{-15} > {-18}

, true.

x = 0

:

{-5} > 7

, false.

Traps:

x > {-4}

forgets the flip,

x > 4

divides by

3

not

{-3}

,

x < {-\tfrac{2}{3}}

subtracts

5

from

7

.

Try it first