Page 103 - Mathematics Coursebook

9.3 Constructing and solving equations

3 Solve each of these equations and check your answers.
a 2a + 3 = 13 b 4a + 1 = 17 c 3a − 2 = 13 d 2a − 8 = 4
e b + 1 = 5 f b + 3 = 7 g b − 2 = 2 h b − 1 = 5
2 4 3 5
c
c
i 14 = 3c + 2 j 29 = 4c − 3 k 9 = + 2 l 1 = − 6
3 6
4 Write an equation for each of these. Solve each equation to find the value of the unknown number.
a ‘I think of a number and add 3. The answer is 18.’
b ‘I think of a number and subtract 4. The answer is 10.’
c ‘I think of a number and multiply it by 4. The answer is 24.’
d ‘I think of a number and divide it by 6. The answer is 12.’
e ‘I think of a number, multiply it by 4 and then add 2. The answer is 26.’
f ‘I think of a number, divide it by 3 and then subtract 8. The answer is 4.’
5 The total length of each set of bricks is shown.
Write an equation involving the lengths of the bricks, then solve your equation.
a a cm a cma cm b b cmb cm b cmb cm b cmb cm
3 cm3 cm
cm
8 cm8 cm
a

20 cm20 cm 24 cm24 cm
6 Kenji has these cards.
4m + 4 2m − 6 6m + 2 = 32 44 20

He chooses one pink card, the purple card and one blue card to make an equation.
Which pink and blue card should he choose to give him the equation with:
a the largest solution for m b the smallest solution for m?
Su
Summary

You should now know that: You should be able to:
+ Terms that contain the same letter or letters are + Simplify an expression by collecting like terms.
called like terms. + Expand a term that includes brackets.
+ To expand a term with brackets you multiply each + Construct and solve linear equations.
term inside the brackets by the term outside the Manipulate numbers, algebraic expressions and
brackets. +
equations.
+ To solve an equation you find the value of the Identify and represent unknown numbers in
unknown letter. +
problems.
+ You can check the solution of an equation is
correct by substituting the number back into the + Work logically and draw simple conclusions.
equation.

102 9 Expressions and equations