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Date ________________________ Section ______
Algebra Proof Problems
Guided Problem: Provide the reason for each step in solving the algebra equation.
4𝑥+7
1. −1 = 𝑥 + 1
1. _________________
2. 4𝑥 + 7 = −(𝑥 + 1) 2. _________________
3. 4𝑥 + 7 = −𝑥 − 1
3. _________________
4. 5𝑥 + 7 = −1
4. _________________
5. 5𝑥 = −8
5. _________________
6. 𝑥 =
−8
5
6. _________________
Use the Given and Prove statements to write an algebraic proof including Statements and Reasons.
6 step (including Given)
A
B
−(𝑥+3)
Given: 10(𝑥 + 10) + 5 ∙ 10 = 200
Given: 4𝑥 + 2𝑥 =
2
Prove: 𝑥 = 5
−3
Prove: 𝑥 =
13
C
𝑥+11
Given: 10 = 2 + 𝑥
Prove: 𝑥 = −1
D
2𝑥+3
Given: 4 = 𝑥 + 7
−25
Prove: 𝑥 = 2
E
Given: 2𝑥 − 8 + 4 = 3𝑥 + 4(2 + 6)
Prove: 𝑥 = −36
F
Given: 4(𝑥 + 3) = 15𝑥 − 1
13
Prove: 𝑥 =
G
Given: 4𝑥 + 2𝑥 − 6 = 2(𝑥 + 1)
Prove: 𝑥 = 2
H
Given: 3𝑥 + 1 + 7 = 5𝑥 − 2 + 2𝑥
5
Prove: 𝑥 =
J
Given: 3(4𝑥 − 5) + 10 = 𝑥 − 27
Prove: 𝑥 = −2
K
Given: 2(3𝑥 + 1) + 11 = 𝑥 − 17
Prove: 𝑥 = −6
L
Given: 2(3𝑥 − 4) + 11 = 𝑥 − 27
Prove: 𝑥 = −6
M
Given: 5(𝑥 + 10) + 5 ∙ 5 = 150
Prove: 𝑥 = 15
N
Given: 𝑥 + 11 = 10(2 + 𝑥)
Prove: 𝑥 = −1
O
Given: 2(𝑥 − 8) + 5 = 3𝑥 − 5
Prove: 𝑥 = −6
P
Given: 4(−2𝑥 + 8𝑎) = 56 and 𝑎 = 3
Prove: 𝑥 = 5
11
2
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Date ________________________ Section ______
5 step (including Given)
1
Given:4𝑥 + 7 = −(𝑥 + 1)
−8
Prove: 𝑥 = 5
2
Given: 2(𝑥 + 1) + 3𝑥 = 10
8
Prove: 𝑥 = 5
3
Given: −5(3𝑥 − 3) = 7𝑥 + 69
27
Prove: 𝑥 = −
4
Given: 5𝑥 − 6 = 𝑦 and 𝑦 = 3𝑥 − 8
Prove: 𝑥 = −1
5
Given: −(4𝑥 + 3 − 12𝑥) = 30
33
Prove: 𝑥 = 8
6
Given: 6(𝑎 + 4) − 2 = 40
Prove: 𝑎 = 3
11
7
8
Given: 2(𝑥 + 6) = 3𝑥 − 10
Prove: 𝑥 = 22
9
10
Given: 2𝑎 + 6𝑏 = 26 and 𝑎 = 4
Prove: 𝑏 = 3
Given: 5𝑥 + 2 = 7𝑥 + 3
−1
Prove: 𝑥 = 2
3𝑥+1
Given: 2 = 2 + 13
29
Prove: 𝑥 = 3
11
Given: 3𝑥 + 𝑦 = 𝑧 + 5 and 𝑧 = 50 and 𝑦 = 5
Prove: 𝑥 = 15
𝑎+𝑏
Given: 3 = 𝑐 and 𝑏 = 𝑎
12
13
Given: 4𝑥 + 8 = 2(𝑥 + 2)
Prove: 𝑥 = −2
14
Given: 2𝑥 + 6 = 4𝑥 − 2
Prove: 𝑥 = 4
15
Given: 4(10𝑥 + 5) − 40 = 160
Prove: 𝑥 = 4.5
16
Given: 2 − 16𝑦 + 11 = −20𝑦 + 15
1
Prove: 𝑦 = 2
17
Given: 2𝑥(4 + 6) − 8 = 12
Prove: 𝑥 = 1
18
Given: 5𝑥 + 4 − 𝑥 + 7 = 88 + 2𝑥
77
Prove: 𝑥 =
Prove: 3𝑐 = 2𝑎
2
4 step (including Given)
a.
Given: 4𝑥 + 7 = −𝑥 − 1
−8
Prove: 𝑥 = 5
𝑥+4
Given:
+ 1 = 10
3
c.
Given: −20𝑦 + 15 = −16𝑦 + 13
1
Prove: 𝑦 =
d.
Given: 𝑦 + 7 = 15 − 3𝑦
Prove: 𝑦 = 2
e.
Given: 6𝑥 + 2 = 2𝑥 − 6
Prove: 𝑥 = −2
Given: 3(𝑥 + 2) = 12
Prove: 𝑥 = 2
2
b.
Prove: 𝑥 = 23
f.
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Date ________________________ Section ______
g.
Given: 5(𝑥 − 2) = 0
Prove: 𝑥 = 2
j.
Given: 5𝑥 + 2 = 7𝑥 − 3𝑥 + 7
Prove: 𝑥 = 5
h.
Given: 2𝑥 = 6 − 3𝑥 + 4
Prove: 𝑥 = 2
k.
1
Given: 𝐴 = 2 (𝐵 − 66)
Prove: 𝐵 = 2𝐴 + 66
l.
Given: 3𝑥 − 3 = 4𝑥 + 12
Prove: 𝑥 = −15
n.
Given: 3𝑥 + 7 = 23 − 𝑥
Prove: 𝑥 = 4
p.
Given: 𝑥 + 𝑥 + 11 = 10
1
Prove: 𝑥 = −
2
r.
Given: 8𝑥 − 11 = 25 − 𝑥
Prove: 𝑥 = 4
t.
Given: −5(𝑥 + 4) = 70
Prove: 𝑥 = −18
m.
Given: 2(𝑥 − 3) = 4
Prove: 𝑥 = 5
o.
Given: 10𝑥 − 10 = 23 − 𝑥
Prove: 𝑥 = 3
q.
Given: 2(3𝑦 + 2) = 11
7
Prove: 𝑥 =
6
s.
Given: 2𝑥 + 5 = 3𝑥 + 2
Prove: 𝑥 = 3
u.
5
Given: 𝐶 = (𝐹 − 32)
9
9
Prove: 𝐹 = 5 𝐶 + 32
w.
Given: 3𝑥(2 + 1) = 36
Prove: 𝑥 = 4
y.
Given: 2𝑥 + 4 = 6 − 2𝑥
1
Prove: 𝑥 = 2
z.
aa.
6𝑥+10
Given:
= 14
2
Given: 10(𝑥 + 1) = 10
Prove: 𝑥 = 0
Prove: 𝑥 = 3
bb.
Given: 2(𝑥 + 4) = 32
Prove: 𝑥 = 12
dd.
Given: 2(𝑥 + 3) = 8
Prove: 𝑥 = 1
ff.
Given: 3(𝑥 − 5) = 12
Prove: 𝑥 = 9
hh.
Given: 5(𝑥 − 3) = 15
Prove: 𝑥 = 6
kk.
Given: 8𝑎 − 20 = 2𝑎 + 22
cc.
Given: 8𝑎 + 12 = −3𝑎 + 34
Prove: 𝑎 = 2
ee.
Given: 4𝑎 + 10 = 2𝑎 + 22
Prove: 𝑎 = 6
gg.
3𝑥+4
Given: 4 = 7
Prove: 𝑥 = 8
jj.
5𝑥−3
Given:
=9
3
Prove: 𝑥 = 6
Ll.
Given: 7(5𝑎 + 2) = 21
Name ____________________________________
Date ________________________ Section ______
1
Prove: 𝑎 = 7
Prove: 𝑎 = 5
mm.
Given: −(7𝑥 − 7) = 42
Prove: 𝑥 = −5
nn.
Given: 5(2𝑥 + 3) = 32
17
Prove: 𝑥 = 10
oo.
Given: 4𝑎 − 10 = 𝑎 + 11
Prove: 𝑎 = 7
qq.
2𝑎−4
Given: 3 = 8
Prove: 𝑎 = 14
ss.
Given: 2(𝑥 − 2) = 10
Prove: 𝑥 = 7
uu.
Given: 12𝑥 − 3 = 3𝑥 + 15
Prove: 𝑥 = 2
yy.
Given: 3𝑥 + 5𝑥 + 4 − 𝑥 + 7 = 88
Prove: 𝑥 = 11
aaa.
Given: 2(𝑚 + 3) = 48
Prove: 𝑚 = 21
pp.
Given: 3(𝑥 + 6) = 36
Prove: 𝑥 = 6
rr.
Given: 𝑥 + 9 = 18 − 2𝑥
Prove: 𝑥 = 3
tt.
Given: 8𝑥 − 3 = 3𝑥 + 17
Prove: 𝑥 = 4
ww.
Given: 9𝑥 + 𝑥 + 50 = 100
Prove: 𝑥 = 5
zz.
Given: −5(𝑥 + 2) = 50
Prove: 𝑥 = −12
3 step (including Given)
I.
Given: 5𝑥 + 7 = −1
−8
Prove: 𝑥 = 5
II.
Given: 4𝑥 + 3 = 15
Prove: 𝑥 = 3
III.
Given: 2𝑥 − 2 = 10
Prove: 𝑥 = 6
IV.
Given: 7𝑥 − 6 = 8
Prove: 𝑥 = 2
V.
𝑛+2
Given:
= 24
4
VI.
Given: −2𝑥 − 20 = 70
Prove: 𝑥 = −45
Prove: 𝑛 = 94
VII.
Prove: 𝑥 = −6
IX.
𝑥+4
Given: 3 = 24
Prove: 𝑥 = 68
VIII.
5
Given: 3 𝑥 + 2 = −8
Given: 10𝑥 − 20 = 50
Prove: 𝑥 = 7
Name ____________________________________
Date ________________________ Section ______
2 step (including Given)
i.
Given: 5𝑥 = −8
−8
Prove: 𝑥 = 5
𝑥
Given: 19 = −7
Prove: 𝑥 = −133
ii.
Given: 𝑥 + 2 = 4
Prove: 𝑥 = 2
iii.
iv.
Given: 𝑥 − 17 = 14
Prove: 𝑥 = 31