Understanding Mathematics, Resource 2, Chapter Nine.6. If I think of a number, halve it, take away 5 and then add on 3 times thenumber I thought of I end up with a number that is 4 more than twice thenumber I first thought of. What was the number I first thought of?7. I think of a number and add it to twice itself. If I then take away one lessthan the number first thought of I end up with an answer of 9. Find thenumber first thought of.8 I think of a number, add 4 and then multiply the answer by 5. I couldhave achieved the same final answer had I instead multiplied my chosennumber by 4 and then added 5. What was the number I thought of?9. If I take a particular number from 3, double the answer and take theresult of doing this from the answer obtained by multiplying the particularnumber by 3 and adding 15, I end up with 25. What is the particularnumber I started with?10. I think of a number, add three, divide the answer by 2 and then add 7This gives an answer that is the same as I would have obtained had Iinstead doubled the number first thought of and then taken away 8. Findthe number first thought ofPls answer whichever you can do!

Answer:   6.  6 is the number I thought of   8.  -15 is the number I thought ofStep-by-step explanation:6. Let x represent the number you thought of.   x/2 . . . halve it   x/2 -5 . . . take away 5 (from the previous result)   x/2 -5 +3x . . . then add on 3 times the number I thought of   = . . . I end up with ...   4 + . . . four more than ...   4 + 2x . . . ... twice the number I first thought of.So, the equation is ...   x/2 -5 +3x = 4 +2xSubtracting 2x we have   x/2 -5 +3x -2x = 4Adding 5 and collecting terms, we get   (3/2)x = 9Multiplying by the inverse of the coefficient of x, we get ...   x = (2/3)(9)   x = 6The number I first thought of was 6.__CheckAfter I halve it, take away 5 and add back 3 times 6, I have ...   3 -5 +18 = 16After I add 4 to twice the number, I have ...   4 +2·6 = 16So, the first set of manipulations gives the same result as the second. 6 is the answer._____8. Let x represent the number I thought of.   x +4 . . . add 4   5(x +4) . . . multiply the answer by 5   = . . . . I could get the same final answer by ...   4x . . . multiplying my number by 4   4x +5 . . . then adding 5So, the equation is ...   5(x +4) = 4x +5   5x +20 = 4x +5 . . . . eliminate parentheses   x + 20 = 5 . . . . . . . . subtract 4x   x = -15 . . . . . . . . . . . subtract 20The number I thought of was -15.__CheckAdd 4 and multiply the result by 5: 5(-15+4) = 5(-11) = -55.Multiply the result by 4 and add 5: 4(-15)+5 = -60+5 = -55, the same final answer.The answer of -15 checks with the problem statement.