Question

What is the simplified form of the expression 3[14 ÷ (42 – 32) – 5]?

Answer 1

\[-\frac{ 54 }{ 5 }\]

Answer 2

hang on im typing how to get it

Answer 3

wait
thats the wrong problem is suppose to be 3[14 ÷ (4 squared – 32 squared) – 5]?

Answer 4

\[3(\left(\begin{matrix}14 \\ 42 - 32\end{matrix} -5\right)\]
substract 32 from 42, gives you 10

\[3 \left(\begin{matrix}14 \\ 10\end{matrix} -5\right)\]

in 14/10, the gcd is 2, so
\[\frac{ 14 }{ 10 } = \frac{ 2x7 }{ 2x5 } = \frac{ 2 }{ 2 } x \frac{ 7 }{ 5 } = \frac{ 7 }{ 5 }\]

\[3\left(\begin{matrix}7 \\ 5\end{matrix} -5\right)\]

put \[\frac{ 7 }{ 5 } -5\] over the common denominator
\[5. \frac{ 7 }{ 5 } + \frac{ 5(-5) }{ 5 } :\]

\[3 \frac{ 7 }{ 5 } + \frac{ -5 x 5 }{ 5 } \]

add the fractons over the common demnominator to a single fraction
\[3 \frac{ 7 - 5x5 }{ 5 }\]

mutiply -5 and 5 togather
\[3 \frac{ -(25 -7) }{ 5 }\]
subtract 7 from 25

\[3x \frac{ -18 }{ 5 }\]

express it as a single fraction
\[\frac{ -18x3 }{ 5 }\]

multiply -18 and 3 togather gives you 54

\[-\frac{ 54 }{ 5 }\]

Answer 5

oh god, lol ok hang on, just seen you typed it wrong

Answer 6

\[-\frac{ 361 }{ 24 }\] for the updated problem, I think, im just starting the squares so I would have someone double check

Answer 7

\[3 \left(\begin{matrix}14 \\ 4^2 -32^2\end {matrix}-5\right) \] if thats what it looks like then
\[-\frac{ 361 }{ 24 }\] is the answer

Answer 8

also as a mixed fraction it would be
\[- 15\frac{ 1 }{ 24 }\]