Solve the following equation: * -9 (t – 2) = 4(t – 15)

Mathematics

1 answer:

iragen [17]3 years ago

5 0

Answer:

6 =t

Step-by-step explanation:

-9 (t – 2) = 4(t – 15)

Distribute

-9t +18 = 4t -60

Add 9t to each side

-9t +18+9t = 4t+9t -60

18 = 13t -60

Add 60 to each side

18+60 = 13t-60+60

78 = 13t

Divide each side by 13

78/13 = 13t/13

6 =t

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Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not

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<u>Answer:</u>

x = 4 (extraneous solution)

<u>Step-by-step explanation:</u>

$\frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\$

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back $x=4$ , we will get two fractions with zero denominator which would be undefined.