Page 102 - Mathematics Coursebook

9.3 Constructing and solving equations

9.3 Constructing and solving equations

To solve an equation, you need to "nd the value of the unknown letter.

You can use inverse
Take the equation: x + 5 = 12 operations to solve
If you take away 5 from both sides of the equation: x + 5 − 5 = 12 − 5 an equation.
you have found the solution to the equation. x = 7

Worked example 9.3
a Solve these equations and check your answers.
i x − 3 = 12 ii 2x + 4 = 16
b Mari thinks of a number, she divides it by 2, then adds 3 and her answer is 7.
i Write an equation for Mari’s unknown number.
ii Solve the equation to fi nd the value of Mari’s number.

a i x = 12 + 3 Add 3 to both sides.
x = 15 Work out the value of x then substitute this value back
Check: 15 − 3 = 12 ! into the equation to check the answer is correct.
ii 2x = 16 − 4 Subtract 4 from both sides.
2x = 12 Simplify the right-hand side.
x = 12 Divide both sides by 2.
2
x = 6 Work out the value of x then substitute this value back
Check: 2 × 6 + 4 = 12 + 4 = 16 ! into the equation to check the answer is correct.

b i n + 3 = 7 Let Mari’s unknown number be n.
2
ii n = 7 − 3 Subtract 3 from both sides.
2
n = 4 Simplify the right-hand side.
2
n = 4 × 2 Multiply both sides by 2.
n = 8 Work out the value of n.

) Exercise 9.3

1 Solve each of these equations and check your answers.
a x + 4 = 11 b x + 3 = 6 c 2 + x = 15 d 7 + x = 19
e x − 4 = 9 f x − 2 = 8 g x − 12 = 14 h x − 18 = 30
i 3x = 12 j 5x = 30 k 7x = 70 l 12x = 72
m x = 4 n x = 5 o x = 3 p x = 7
2 3 7 9
2 Dayita uses this method to solve an equation when the
unknown is on the right-hand side of the equation. Solve the equation: 12 = y + 3
Use Dayita’s method to solve these equations. Write this as: y + 3 = 12
Solve as normal: y = 12 – 3
−
3
− 3
a 15 = y + 3 b 9 = y + 2 c 13 = y − 5 d 25 = y − 3

y y y = 9
e 24 = 8y f 42 = 6y g 5 = h 7 =
2 5

9 Expressions and equations 101