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Question

# (a) Complete the table and by inspection of the table, find the solution to the equation m + 10 = 16. m 1 2 3 4 5 6 7 8 9 10 … m + 10 − − − − − − − − − − − (b) Complete the table and by inspection of the table, find the solution to the equation 5t = 35. t 3 4 5 6 7 8 9 10 11 … 5t − − − − − − − − − − (c) Complete the table and find the solution of the equation z/3 = 4 using the table. z 8 9 10 11 12 13 14 15 16 ... 3 − − − − − − − (d) Complete the table and find the solution to the equation m − 7 = 3 m 5 6 7 8 9 10 11 12 13 … m − 7 − − − − − − − − − −

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Solution

## (a) For m + 10, the table can be constructed as follows. m m + 10 1 1 + 10 = 11 2 2 + 10 = 12 3 3 + 10 = 13 4 4 + 10 = 14 5 5 + 10 = 15 6 6 + 10 = 16 7 7 + 10 = 17 8 8 + 10 = 18 9 9 + 10 = 19 10 10 + 10 = 20 By inspection, we can find that m = 6 is the solution of the above equation as for m = 6, m + 10 = 6 + 10 = 16 (b) For 5t, the table can be constructed as follows. t 5t 3 5 × 3 = 15 4 5 × 4 = 20 5 5 × 5 = 25 6 5 × 6 = 30 7 5 × 7 = 35 8 5 × 8 = 40 9 5 × 9 = 45 10 5 × 10 = 50 11 5 ×11 = 55 By inspection, we can find that t = 7 is the solution of the above equation as for t = 7, 5t = 5 × 7 = 35 (c) For , the table can be constructed as follows. z 8 9 10 11 12 13 14 15 16 By inspection, we can find that z = 12 is the solution of the above equation as for z = 12, = 4 (d) For m − 7, the table can be constructed as follows. m m − 7 5 5 − 7 = − 2 6 6 − 7 = − 1 7 7 − 7 = 0 8 8 − 7 = 1 9 9 − 7 = 2 10 10 − 7 = 3 11 11 − 7 = 4 12 12 − 7 = 5 13 13 − 7 = 6 By inspection, we can find that m = 10 is the solution of the above equation as for m = 10, m − 7 = 10 − 7 = 3

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