DE bisects BC. If BC = 5x - 3 and CE = 2x + 25, find the value of x
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5x-3 = 2(2x+25)
To find the value of x, we can use the fact that DE bisects BC. This means that the lengths of BD and EC are equal.
Let's set up an equation using this information:
BD = EC
The length of BD is equal to the length of BC minus the length of CD :
BD = BC - CD
We know that BC is equal to 5x - 3, and we need to find the value of CD. Since DE bisects BC, CD is equal to CE.
CD = CE = 2x + 25
Substituting these values into our equation, we have:
BD = BC - CD
BD = (5x - 3) - (2x + 25)
Simplifying this equation, we get:
BD = 5x - 3 - 2x - 25
BD = 3x - 28
Since DE bisects BC, BD is equal to CE. This means:
CE = 3x - 28
Since BD = CE, we can equate the two expressions:
3x - 28 = 2x + 25
Solving this equation for x will give us the value we are looking for:
3x - 2x = 25 + 28
x = 53
Therefore, the value of x is 53.