Page 51 - 新思维数学学生用书7 样章

2 Expressions, formulae and equations

2.5 Constructing and solving equations

In this section you will … Key words

• write and use equations. solution

solve
To solve an equation, you need to find the value of the unknown letter.
Consider the equation: x + 5 = 12

Subtract 5 from both sides of the equation: x + 5 − 5 = 12 − 5
You have found the solution to the equation: x = 7

Worked example 2.5

Solve these equations and check your answers.
a x − 3 = 12 b 2y + 4 = 16

Answer
a x − 3 + 3 = 12 + 3 Add 3 to both sides.

x = 15 Work out the value of x, then substitute this
value back into the equation to check that the
answer is correct.

Check: 15 − 3 = 12 ✓
b 2y = 16 − 4 Subtract 4 from both sides.
2y = 12 Simplify the right-hand side.

y = 12 Divide both sides by 2.
2
y = 6 Work out the value of y, then substitute this
value back into the equation to check that the
answer is correct.

Check: 2 × 6 + 4 = 12 + 4 = 16 ✓

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