There are two parts to this question. Part a) Complete the number machine so that the output is 𝑛 is equal to negative three 𝑥 plus five. Part b) Write down the output 𝑠 in terms of the input 𝑡.
In the first part of the question, we are told that the output is negative three 𝑥 plus five. We can complete the number machine by finding the two steps that take us from 𝑥 to this expression.
The first thing that we are doing to 𝑥 is multiplying it by negative three, as 𝑥 multiplied by negative three is equal to negative three 𝑥. Our second step to get to the expression negative three 𝑥 plus five is adding five. The two operations that we perform to get from an input 𝑥 to an output negative three 𝑥 plus five are multiply it by negative three and add five. We must make sure we do these in the correct order, as adding five and then multiplying by negative three would not give the same expression.
In the second part of the question, we need to write down the output 𝑠 in terms of the input 𝑡. The first operation in this case is subtract or minus two. As our input is 𝑡, this would give us 𝑡 minus two. The second operation was multiplied by four. Therefore, we need to multiply 𝑡 minus two by four. It is important that we put the 𝑡 minus two in brackets, as we must do this calculation first, remembering our order of operations BIDMAS. Brackets come before multiplication.
When multiplying a bracket by a number, we write the number before the bracket, as shown. This means that our output 𝑠 is equal to four multiplied by 𝑡 minus two. We could multiply out or expand the bracket. However, in this case, there is no need.
If we had decided to expand the bracket, we would need to multiply four by 𝑡 and four by negative two. This would give us four 𝑡 minus eight, as four multiplied by 𝑡 is four 𝑡 and four multiplied by negative two is negative eight. Either of these answers would get the full marks in this question.