PRACTICE: Mixed practice with the distributive property
EXAMPLES: Here I’ve used the operation inside the parentheses as the
operation in your answer and then cleaned up extra negatives at the end
(changing any “plus a negative” to “–“ and changing any double negatives to a “+”).
4(2x + 6)
= 4(2x) + 4(6)
= 8x + 24
–9(2x – 3)
= –9(2x) – (–9)(3)
= –18x – (–27)
= –18x + 27
LEVEL 1
LEVEL 2
3
8(4x – 5)
= 8(4x) – 8(5)
=32x – 40
LEVEL 1
7
=
=
(x – 14)
3
7
3
7
x –
3
7
x –6
(14)
LEVEL 2
one method: Cover over the
4 here so it looks as if the
subtraction after it is a
negative sign. Then
distribute the negative as in
the level 2 problem here.
Put the 4 back and finish.
4 – 6(3x – 5)
=4
–6(3x) – (–6)(5)
=4
–18x + 30
= – 18x + 34
another method: Rewrite
the problem with “plus a
negative” instead of
subtraction after the 4 so
you don’t lose the negative:
–8(–4x – 5)
= –8(–4x) – (–8)(5)
= 32x – (–40)
= 32x + 40
4 + –6(3x – 5)
= 4 + –6(3x) – (–6)(5)
= 4 + –18x + 30
= –18x + 34
LEVEL 3
LEVEL 3
LEVEL 1 (whole numbers)
1) 4(x + 6)
8(4x + 5)
9(2x + 3)
2) 5(x – 7)
6(5x – 3)
7(3x – 2)
D. Stark 1/30/2017
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LEVEL 2 (integers; fractions)
3) –3(5x + 9)
–10(2x + 4)
–11(–4x + 5)
4) –8(6x – 4)
–4(3x – 3)
9(–4x – 8)
5)
2
5
(x – 5)
–
1
3
(9x + 15)
2
3
(–3x – 5)
LEVEL 3 (messy negatives)
6) –4(–3x – 5)
–7(–x – 4)
–9.6(–2.1x – 5.3)
7) 5 – 4(2x – 6)
–4 – 5(3x – 7)
12.8 – 6(1.2x – 8.4)
D. Stark 1/30/2017
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PRACTICE: Mixed practice with the distributive property
LEVEL 1 (whole numbers)
KEY
1) 4(x + 6)
= 4x + 4(6)
8(4x + 5)
= 8(4x) + 8(5)
9(2x + 3)
= 9(2x) + 9(3)
= 4x + 24
= 32x + 40
= 18x + 27
2) 5(x – 7)
= 5x – 5(7)
6(5x – 3)
= 6(5x) – 6(3)
7(3x – 2)
= 7(3x) – 7(2)
= 5x – 35
= 30x – 18
= 21x – 14
LEVEL 2 (integers; fractions)
3) –3(5x + 9)
= –3(5x) + –3(9)
= –15x + –27
–10(2x + 4)
= –10(2x) + –10(4)
= –20x + –40
–11(–4x + 5)
= –11(–4x) + –11(5)
= 44x + –55
= –15x – 27
= –20x – 40
= 44x – 55
4) –8(6x – 4)
= –8(6x) – (–8)(4)
–4(3x – 3)
= –4(3x) – (–4)(3)
9(–4x – 8)
= 9(–4x) – (9)(8)
= –48x + 32
= –12x + 12
= –36x – 72
5)
2
(x – 5)
5
𝟐
𝟐
= x – (5)
𝟓
𝟓
=
𝟐
𝟓
x–2
–
1
3
= –
2
(9x + 15)
𝟏
𝟑
(9x) + –
= –3x + –5
= –3x – 5
𝟏
𝟑
3
(15)
=
(–3x – 5)
𝟐
𝟑
(–3x) –
= –2x –
𝟐
𝟑
(5)
𝟏𝟎
𝟑
D. Stark 1/30/2017
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LEVEL 3 (messy negatives)
6) –4(–3x – 5)
= –4(–3x) – (–4)(5)
= 12x – (–20)
–7(–x – 4)
= –7(–x) – (–7)(4)
= 7x – (–28)
= 12x + 20
= 7x + 28
–9.6(–2.1x – 5.3)
= –9.6(–2.1x) – (–
9.6)(5.3)
= 20.16x – (–50.88)
= 20.16x + 50.88
7) 5 – 4(2x – 6)
= 5 – 4(2x) – (–4)(6)
= 5 – 8x – (–24)
= 5 – 8x + 24
–4 – 5(3x – 7)
= –4 – 5(3x) – (–5)(7)
= –4 – 15x – (–35)
= –4 – 15x + 35
12.8 – 6(1.2x – 8.4)
= –8x + 29
= –15x + 31
= –7.2x + 63.2
You might find it easier to
rewrite the problem with
“plus a negative” instead of
subtraction so you don’t
lose the distributed
negative:
You might find it easier to
rewrite the problem with
“plus a negative” instead of
subtraction so you don’t
lose the distributed
negative:
You might find it easier to
rewrite the problem with “plus
a negative” instead of
subtraction so you don’t lose
the distributed negative:
5 + –4(2x – 6)
= 5 + (–4)(2x) – (–4)(6)
= 5 + –8x – (–24)
= 5 – 8x + 24
–4 + –5(3x – 7)
= –8x + 29
= –15x + 31
= –4 + (–5)(3x) – (–5)(7)
= –4 + –15x – (–35)
= –4 + –15x + 35
= 12.8 – 6(1.2x) – (–6)(8.4)
= 12.8 – 7.2x – (–50.4)
= 12.8 – 7.2x + 50.4
12.8 + –6(1.2x – 8.4)
= 12.8 + (–6)(1.2x) – (–6)(8.4)
= 12.8 + –7.2x – (–50.4)
= 12.8 + –7.2x + 50.4
= –7.2x + 63.2
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