9514 1404 393
Answer:
BD = 17
Step-by-step explanation:
The Pythagorean theorem can be used twice:
BC^2 + AC^2 = AB^2
BC = √(AB^2 -AC^2) = √(25^2 -24^2) = √49 = 7
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Likewise, ...
DC = √(AD^2 -AC^2) = √(26^2 -24^2) = √100 = 10
Then ...
BD = BC +DC = 7 + 10
BD = 17
Subtract 14x from both sides to get
Subtract 12 from both sides to get
Now we have moved all terms involving x on one side, and all constant terms on the other. We can simplift both sides, i.e. sum like terms, to get
Now we have to divide both sides by 6. When dealing with inequality you have to be careful about dividing both sides by the same constant: if the constant is negative, the inequality side switches (i.e. ). But this is not the case since 6 is positive, so we mantain the inequality sign:
on the other. We can simplift both sides, i.e. sum like terms, to get
Evaluate left and right hand side:
