How do you solve 4t2>12?

2 Answers
Mar 10, 2018

t>3 OR t<3

Explanation:

We have the inequality:

4t2>12

1) Divide both sides by 4:

4t24>124

t2>3

2) Take the square root of both sides:

t2>3

t>3

BUT square roots have two solutions - positive or negative. You know that, when we divide by a negative, we change the sign of the inequality. So:

t>3 OR t<3

Mar 10, 2018

The solution is t(,3)(3,+)

Explanation:

Let's rearrange the inequality

4t2>12

4t212>0

Factorise,

4(t23)>0

4(t+3)(t3)>0

Let f(t)=4(t+3)(t3)

Now build a sign chart

aaaataaaaaaaaaa3aaaa3aaaa+

aaaat+3aaaaaaaaaaa+aaaa+

aaaat3aaaaaaaaaaaaaaa+

aaaaf(t)aaaaaaaaaa+aaaaaaaa+

Therefore,

f(t)>0 when t(,3)(3,+)

graph{4x^2-12 [-25.65, 25.66, -12.83, 12.84]}