Algebra Foundations for Normal People by Gabriel Beguerie - HTML preview

Chapter 6

Worked example (no skipped steps)

6.1 Solve 𝑥 + 9 = 14.

Subtract 9:

𝑥 = 5

Worked example (no skipped steps)

6.2 Solve 𝑦 − 6 = 11.

Add 6:

𝑦 = 17

156

Step-by-step solutions

Worked example (no skipped steps)

6.3 Solve 4 𝑚 = 28.

Divide by 4:

𝑚 = 7

Worked example (no skipped steps)

6.4 Solve 𝑝 = 3.

5

Multiply by 5:

𝑝 = 15

Worked example (no skipped steps)

6.5 Solve 2 𝑥 + 7 = 23.

Subtract 7:

2 𝑥 = 16

Divide by 2:

𝑥 = 8

Worked example (no skipped steps)

6.6 Solve 3 𝑎 − 4 = 11.

Add 4:

3 𝑎 = 15

Divide by 3:

𝑎 = 5

Worked example (no skipped steps)

6.7 Solve 𝑡 + 2 = 6.

3

Subtract 2:

𝑡 = 4

3

Multiply by 3:

𝑡 = 12

Worked example (no skipped steps)

6.8 Solve 5 − 2 𝑘 = 17.

Subtract 5:

−2 𝑘 = 12

Divide by −2:

𝑘 = −6

Chapter 6

157

Worked example (no skipped steps)

6.9 Solve 𝑥 − 11 = −4.

Add 11 to both sides:

𝑥 − 11 + 11 = −4 + 11

So:

𝑥 = 7

Check: 7 − 11 = −4.

Worked example (no skipped steps)

6.10 Solve −5 𝑦 = 35.

Divide both sides by −5:

−5 𝑦

35

=

−5

−5

So:

𝑦 = −7

Check: −5(−7) = 35.

Worked example (no skipped steps)

6.11 Solve 4 𝑚 − 9 = 19.

Add 9 to both sides:

4 𝑚 − 9 + 9 = 19 + 9

4 𝑚 = 28

Now divide by 4:

4 𝑚

28

=

4

4

𝑚 = 7

Check: 4(7) − 9 = 28 − 9 = 19.

Worked example (no skipped steps)

6.12 Solve 𝑧 − 2 = 3.

7

Add 2 to both sides:

𝑧 − 2 + 2 = 3 + 2

7

𝑧 = 5

7

Now multiply both sides by 7:

𝑧

7 ·

= 7 · 5

7

𝑧 = 35

Check: 35 − 2 = 5 − 2 = 3.

7

158

Step-by-step solutions

Worked example (no skipped steps)

6.13 Solve 𝑥 = 5.

4

Multiply both sides by 4:

𝑥 = 20

Answer: 𝑥 = 20.

Worked example (no skipped steps)

6.14 Solve 3 𝑦 − 2 = 16.

Add 2:

3 𝑦 = 18

Divide by 3:

𝑦 = 6

Answer: 𝑦 = 6.

Worked example (no skipped steps)

6.15 Solve 2 𝑚 + 9 = 23.

Subtract 9:

2 𝑚 = 14

Divide by 2:

𝑚 = 7

Answer: 𝑚 = 7.

Worked example (no skipped steps)

6.16 Solve 𝑛 + 4 = 9.

3

Subtract 4:

𝑛 = 5

3

Multiply by 3:

𝑛 = 15

Answer: 𝑛 = 15.

Worked example (no skipped steps)

6.17 Solve 5 − 𝑝 = 11.

Subtract 5:

− 𝑝 = 6

Multiply by −1:

𝑝 = −6

Answer: 𝑝 = −6.

Chapter 7

159

Worked example (no skipped steps)

6.18 Solve −2 𝑥 = 14.

Divide by −2:

𝑥 = −7

Answer: 𝑥 = −7.

Worked example (no skipped steps)

6.19 Solve 7 𝑘 + 5 = 40.

Subtract 5:

7 𝑘 = 35

Divide by 7:

𝑘 = 5

Answer: 𝑘 = 5.

Worked example (no skipped steps)

6.20 Solve 𝑎 − 3 = 1.

5

Add 3:

𝑎 = 4

5

Multiply by 5:

𝑎 = 20

Answer: 𝑎 = 20.