Solve for equation for ex in term of c 2/3(x+1/2) - 1/4=5/2

1 answer:

4 0

$\dfrac{2}{3}\left(x+\dfrac{1}{2}\right)-\dfrac{1}{4}=\dfrac{5}{2}\qquad|\text{use distributive property}\\\\\dfrac{2}{3}x+\dfrac{2}{3}\cdot\dfrac{1}{2}-\dfrac{1}{4}=\dfrac{5}{2}\\\\\dfrac{2}{3}x+\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{5}{2}\qquad|\text{multiply both sides by LCM(2,\ 3,\ 4)=12}\\\\12\cdot\dfrac{2}{3}x+12\cdot\dfrac{1}{3}-12\cdot\dfrac{1}{4}=12\cdot\dfrac{5}{2}\\\\4\cdot2x+4-3=6\cdot5\\\\8x+1=30\qquad|\text{subtract 1 from both sides}\\\\8x=29\qquad|\text{divide both sides by 8}\\\\x=\dfrac{29}{8}$

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Answer:

Both 16 and 1 are squares. This suggests using the formula for the difference of squares. Answer link.

Step-by-step explanation:

Every time you have a difference in the format of

A2−B2 you can factor as (A−B)(A+B).

Then you have to identify if your quantity is the difference of two squared quantities.

It is. In fact we can write it as: