Question

Can someone please show me step by step how to do these types of problems? I'm so lost and stressed out. Please help?! Will fan and medal.

Answer 1

Solve for x: −2x + 5 < 7

x > −1

x < −1

x > −6

x < −6

Answer 2

Well we want to isolate x (have x on only one side of the equation).

So firstly, we can move 5 over to the right side of the equation by subtracting 5 from both sides:

-2x+5-5 < 7 -5
-2x < 2

Answer 3

Now, we want to get rid of that -2 in front of the x... we can do this by dividing both sides by -2, but there is a catch. Whenever you divide by a negative number, you must CHANGE the direction of the inequality!

-2x < 2

turns into

(-2x)/(-2) > 2/(-2)

x > -1

notice how the < was swapped to >

Answer 4

timely beat me to it, but I'll continue anyways


The goal is to completely isolate x. We do this by undoing the order of operations (basically follow PEMDAS in reverse)

So we first undo the +5 by subtracting 5 from both sides

−2x + 5 < 7

−2x + 5 - 5 < 7 - 5

−2x + 0 < 2

-2x < 2


Then we divide both sides by -2 to undo the multiplication of -2 with x. This will flip the inequality sign (because we're dividing both sides by a negative number)

-2x < 2

-2x/(-2) > 2/(-2) ... Notice how the inequality sign changed directions

1x/1 > -1

1x > -1

x > -1

The variable x is now all by itself on one side, so we're done.

Answer 5

Solving for variables in these types of equations is just like what you have been learning in algebra with the equal sign (=)

The only thing you need to remember is to change the direction of the inequality if you multiply or divide the equation by a negative number!

Does this make sense to you?

Answer 6

Yes, it does. Thank you guys sooooo much! @timely @jim_thompson5910