ALGEBRA-1E:) CLASS:DATE:rer all questions. Show your working neatly.Given that (x- pXx-5)=x-qx+15, find the value of p and q.-- If x=3 is a solution of the equation x+ px+12 0, find the value of p. Hence find the othersolution of the equation.3. If one of the roots of the equation x-5x+k 0is 2, find the value of k. Hence find the otherroot of the equation.4. Marc is 3 times as old as his brother, John. The sum of the squares of their ages two years agowas 178. If John is x years old, form an equation in x and show that it reducesto 5x - 8x-85 = 0. Solve this equation to find their present ages.5. PQRS is a rectangle in which PQ = (x+2)cm and PS =(a) If the area of the rectangle PQRS is 88 cm?, write down in terms of x and show that itreduces to 2x +3-90= 0.(b) Solve this equation for x and find the dimensions of the rectangle.(2x-1)cm.6. A motorist travelled from Town A to Town B which was 135 km apart. After travelling 60 kmat an average speed of x km/h, he increased his average speed by 10 km/h for the remainingjourney. He took 3 hours to complete his journey.(a) Form an equation in terms of x and show that it reduces to x-35x-200 = 0.(b) Solve this equation to find the value x. Hence, find the time taken for the second part of thejourney.7. A bookseller bought x cookbooks for $24.(a) Write down an expression, in terms of x, for the cost price of each book.(b) He sold 6 books with a profit of $2 each. Write down an expression, in terms of x, for theselling price of each of these books.(c) He sold the rest of the books at $4 each. If he received $38 for selling all the books, writedown an equation in terms of x and show that it reduces to 2.x-25x+72 =0.(d) Solve this equation for x and find the number of cookbooks the bookseller bought.END

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- Given that (x- pXx-5)%3Dx-qx+15, find the value of p and q.