Problem of the Week

Updated at Jun 15, 2020 10:33 AM

This week we have another equation problem:

How can we solve the equation 4(3−53−n)=224(3-\frac{5}{3-n})=22?

Let's start!



4(3−53−n)=224(3-\frac{5}{3-n})=22

1
Divide both sides by 44.
3−53−n=2243-\frac{5}{3-n}=\frac{22}{4}

2
Simplify  224\frac{22}{4}  to  112\frac{11}{2}.
3−53−n=1123-\frac{5}{3-n}=\frac{11}{2}

3
Subtract 33 from both sides.
−53−n=112−3-\frac{5}{3-n}=\frac{11}{2}-3

4
Simplify  112−3\frac{11}{2}-3  to  52\frac{5}{2}.
−53−n=52-\frac{5}{3-n}=\frac{5}{2}

5
Multiply both sides by 3−n3-n.
−5=52(3−n)-5=\frac{5}{2}(3-n)

6
Simplify  52(3−n)\frac{5}{2}(3-n)  to  5(3−n)2\frac{5(3-n)}{2}.
−5=5(3−n)2-5=\frac{5(3-n)}{2}

7
Multiply both sides by 22.
−5×2=5(3−n)-5\times 2=5(3-n)

8
Simplify  −5×2-5\times 2  to  −10-10.
−10=5(3−n)-10=5(3-n)

9
Divide both sides by 55.
−105=3−n-\frac{10}{5}=3-n

10
Simplify  105\frac{10}{5}  to  22.
−2=3−n-2=3-n

11
Subtract 33 from both sides.
−2−3=−n-2-3=-n

12
Simplify  −2−3-2-3  to  −5-5.
−5=−n-5=-n

13
Multiply both sides by −1-1.
5=n5=n

14
Switch sides.
n=5n=5

Done
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