algebra

Find the value of \(w\) in the following equations:
\(3x-2y+w=11\)
\(x+5y-2w=-9\)
\(2x+y-3w=-6\)

Solve for the value of \(x\).
\(2x-y+z=6\)
\(x-3y-2z=13\)
\(2x-3y-3z=16\)

Solve for \(x\): \(\sqrt{x+2\sqrt{2x+3}}-3=0\)

Solve for \(x\) from the given equation:
\(\sqrt[4]{8\sqrt[3]{2\sqrt{8x}}}=2\)

The expression \(x^4+ax^3+5x^2+bx+6\) when divided by \((x-2)\) leaves a remainder of \(16\) and when divided by \((x+1)\) leaves a remainder of \(10\). Find \(a\) and \(b\).

Find the \(6^{th}\) term of the expansion of \((\frac{1}{2a}-3)^{16}\)

Solve for the value of \(x\) in the following equation: \(x^{3 \log x} = 100x\)

Given: \(\log 6 + x \log 4 = \log 4 + \log(32+4^x)\). Find \(x\).

At present, the sum of the parents' ages is twice the sum of the children's ages. Five years ago, the sum of the parents' ages was \(4\) times the sum of the children's ages. Fifteen years hence, the sum of the parents' ages will be equal to the sum of the children's ages. How many children are there?

On one job, two power shovels excavate \(20{,}000\) cubic meters of earth, the larger shovel working \(40\) hours and the smaller for \(35\) hours. On another job, they removed \(40{,}000\) cubic meters with the larger shovel working \(70\) hours and the smaller working \(90\) hours. How much earth can each remove in \(1\) hour working alone?

A boat man rows to a place \(4.8\) miles with the stream and back in \(14\) hours, but finds that he can row \(14\) miles with the stream in the same time as \(3\) miles against the stream. Find the rate of the stream.

A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at \(3/5\) of its former rate and arrives three hour after time; but had the accident happened \(50\) miles farther on the line, it would have arrived one and one-half hour sooner. Find the length of the journey.

A man left his home at past 3:00 o'clock PM as indicated in his wall clock, between 2 to 3 hours after, he returns home and noticed the hands of the clock interchanged. At what time did the man leave his home?

A group of EE examinees decided to hire a mathematics tutor from Excel Review Center and planned to contribute equal amount for the tutor's fee. If there were 10 more examinees, each would have paid P 2 less. However, if there were 5 less examinees, each would have paid P 2 more. How many examinees are there in the group?

In the recent "Gulf War" in the Middle East, the allied forces captured 6400 of Saddam's soldiers and with provisions on hand it will last for 216 meals while feeding 3 meals a day. The provision lasted 9 more days because of daily deaths. At an average, how many died per day?

The \(3^{rd}\) term of a harmonic progression is 15 and the \(9^{th}\) term is 6. Find the \(11^{th}\) term.