Problem of the Week

Updated at Jan 7, 2019 2:41 PM

For this week we've brought you this equation problem.

How would you solve 4t−5−5t=124t-5-\frac{5}{t}=\frac{1}{2}?

Here are the steps:



4t−5−5t=124t-5-\frac{5}{t}=\frac{1}{2}

1
Multiply both sides by 2t2t.
8t2−10t−10=t8{t}^{2}-10t-10=t

2
Move all terms to one side.
8t2−10t−10−t=08{t}^{2}-10t-10-t=0

3
Simplify  8t2−10t−10−t8{t}^{2}-10t-10-t  to  8t2−11t−108{t}^{2}-11t-10.
8t2−11t−10=08{t}^{2}-11t-10=0

4
Split the second term in 8t2−11t−108{t}^{2}-11t-10 into two terms.
8t2+5t−16t−10=08{t}^{2}+5t-16t-10=0

5
Factor out common terms in the first two terms, then in the last two terms.
t(8t+5)−2(8t+5)=0t(8t+5)-2(8t+5)=0

6
Factor out the common term 8t+58t+5.
(8t+5)(t−2)=0(8t+5)(t-2)=0

7
Solve for tt.
t=−58,2t=-\frac{5}{8},2

Done

Decimal Form: -0.625, 2
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