Page 54 - 新思维数学学生用书7 样章

2.5 Constructing and solving equations

9 The diagrams show the lengths of the equal sides of these isosceles triangles.
For each triangle:
i Write an equation. ii Solve your equation to find the value of p.
a b c

2p + 1 14 4p–5 37 26 6p–10

10 a Write an equation for each of these situations.
i Paul has some DVDs. He sells three of the DVDs. He has 26 DVDs left.
ii Yaz has some books. She buys five more books. She now has 18 books.

iii On Monday, Nial goes for a bike ride. On Tuesday he rides twice as far as he did on
Monday. On Tuesday he rides 48 km.
iv Jana’s age is three more than twice the age of Jin. Jana is 35 years old.
b Solve your equations in part a to answer the following questions.

i How many DVDs does Paul have to start with?
ii How many books does Yaz have to start with?
iii How far does Nial ride on Monday?

iv How old is Jin?

Activity 2.3

Work in pairs for this activity.

On a piece of paper, write down four situations like the ones in Question 10.
Swap your paper with another pair of learners.
Write down an equation for each of the situations you have been given.
Solve each of the equations.

Swap back your pieces of paper and mark each other’s work.
Discuss any mistakes that have been made.

11 Kenji has the following cards.

4m + 4 2m– 6 6m +2 = 32 44 20

He chooses one blue card, the red card and one yellow card to make an equation.
Which blue and yellow card should he choose to give him the equation with:
a the largest solution for m?

b the smallest solution for m?
Explain your decisions and show that your answers are correct.

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