Question

Solve: -2t + 7 – 5t ≥ 3 + 4t + 10.
A. t ≤ -20/7
B. t ≤ -6/11
C. t ≥ -20/7
D. t ≥ -6/11

Answer 1

@johnweldon1993

Answer 2

Hello again :)

\[\large -2t + 7 - 5t \ge 3 + 4t + 10\]

We need to combine like terms here...look how we have \(\large -2t - 5t\) on the left hand side...and notice how we have 3 + 10 on the right hand side...lets simplify that...

Answer 3

-7t and 13

Answer 4

Right...so we have

\[\large -7t + 7 \ge 4t + 13\]

Now we want o continue to combine like terms..but by getting the like terms on 1 side...

So we want all the terms with a 't' on 1 side...and all the ones without..on the other..

So lets subtract 7 from both sides of this equation...and then subtract 4t from both sides...what do we have then?

Answer 5

7>13

Answer 6

wait

Answer 7

I'm waiting ... :)

Answer 8

idk im lost i know i did something wrong

Answer 9

ok explain you take 7 form both sides frist right

Answer 10

Here I already typed out the explanation :)

Not quite...so we would have

\[\large -7t + 7 \ge 4t + 13\]

We want to subtract 7 from both sides of the equation

\[\large -7t + 7 \color \red{- 7} \ge 4t + 13 \color \red{-7}\]
which will give us

\[\large -7t \ge 4t + 6\]

Now we want to subtract 4t from both sides of the equation

\[\large -7t \color \red{-4t}\ge 4t \color \red{-4t} + 6\]
Which will then give us

\[\large -11t \ge 6\]

Answer 11

but then thats the answer which one is it ?

Answer 12

That isn't the answer...remember we want to solve for 't'...not -11t

So we need to divide both sides of that equation by -11

\[\large t \le -\frac{6}{11}\]

****************notice what happened with the sign there....*******************

We HAD \(\ge\) but we ended with \(\le\) this is because we divided by a negative number...when that happens we switch the direction of the sign

Answer 13

Your lots of help i really like how your explaining everything

Answer 14

Glad to help :)