Mathematics 30 June 1999 Grade 12 Diploma Exam
Mathematics 30 June 1999 Grade 12 Diploma Exam
Mathematics 30 June 1999 Grade 12 Diploma Exam
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Use the following information to answer the next question.<br />
A mathematics class was asked to solve the equation<br />
3 x + 2 = 6 x<br />
The attempts of two students to solve the equation are shown below. Each<br />
student made one error that led to an incorrect solution.<br />
Student A<br />
Student B<br />
3 x + 2 =6 x 3 x + 2 =6 x<br />
3 x + 2 =3 2x log 3 x + 2 = log 6 x<br />
x + 2 = 2x x + 2 log 3 = x log 6<br />
2=2x – x 2 log 3 = –x + x log 6<br />
x =2 2 log 3=x(–1 + log 6)<br />
2log3<br />
( −1<br />
+ log6)<br />
= x<br />
x is approximately – 4.3<br />
Written Response—10%<br />
3. • Show that neither x = 2 nor x = – 4.3 satisfies the equation 3 x + 2 = 6 x .<br />
<strong>30</strong>
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