4. Find the value of the variable in each of the following and verify your answer. (i) 2(r + 3) = r + 7 (ii) 5(2q − 1) = 3q + 9 (iii) 3(k − 1) = 2(k + 1)
5. Find the value of the variable in each of the following and verify your answer. (i)
_ 5 = 7
y (ii) x (iii)
_ 2 = 8
_t 7 = 11
_ 3 = 20
(iv) n
_ 14 = 9
(v) v + 6 (vi) 9 − c
_ 9 = 21
_ 10 = 9
6. Find the value of the variable in each of the following and verify your answer. (i) 12k
(ii) 9g
_ 4 = 18
(iii) 4f + 4
_ 2 = 22
(iv) 7d + 13 (v) 5t − 8
_ 5 = 11
_ 9 = 8
(vi) 2w + 10
_ 3 = 24
9.4 Creating and solving linear equations
(vii) 15 − h (viii) 6 + n (ix) x − 22
_ −16 = 8
_ −12 = −13
_ −24 = 17
By the end of this section you should be able to: ● generate and solve linear equations using variables
A linear equation is an algebraic equation in which the highest power of the variables is 1. When graphed, a linear equation is represented by a straight line.
Many mathematical problems begin as word problems. To solve a mathematical word problem, the words must be analysed and turned into a mathematical expression. Once we have done this, it becomes much easier to work with.
There are many problems that involve relationships among known and unknown numbers (variables). These can be put in the form of equations. The equations are generally stated in words and it is for this reason we refer to these problems as ‘word’ problems.
Section A Introducing concepts and building skills 143