L is a point on . CN = 85, CL = 32 – x and LN = 4x – 7. What is CL?
To find the value of CL, we can use the given information about the lengths of CN, CL, and LN.
Given: CN = 85, CL = 32 – x, and LN = 4x – 7.
We know that CN + LN = CL, since the total length of CL must be equal to the sum of the lengths of CN and LN.
Substituting the given values, we have:
85 + (4x – 7) = 32 – x
Now, let's solve this equation step by step to find the value of x:
85 + 4x – 7 = 32 – x
Collecting like terms:
4x – x = 32 – 85 + 7
3x = -46
Dividing both sides by 3:
x = -46/3
Now that we have the value of x, we can substitute it back into the equation for CL to find its value:
CL = 32 – x
CL = 32 – (-46/3)
To simplify -(-46/3), we can rewrite it as 46/3:
CL = 32 + 46/3
To add these fractions, we need a common denominator:
CL = (32 * 3) + 46/3
CL = 96 + 46/3
Now, let's convert the mixed fraction into an improper fraction:
CL = (96 * 3)/3 + 46/3
CL = 288/3 + 46/3
Adding the fractions:
CL = (288 + 46)/3
CL = 334/3
Therefore, CL = 334/3 or approximately 111.33.