x - Berkeley City College

1. Solve the equation:
a. −6x = 3
1
2
b. x − 5 = 10
ans: x = −
ans: x = 15
c. 3x − 7 = 12
19
ans: x =
3
d. 3x + 2 = 5x − 1
3
ans: x =
2
e. 4 − 2(x + 1) = 5x + 2
ans: x = 0
f. 4 − 5(x + 1) = 4
ans: x = −1
g. −3(x − 4) + 4x + 3 = 5x − 2(x + 3)
21
2
h. 4 − 2(x + 1) = 5x + 2
ans: x =
ans: x = 0
i. 12x − 2(x − 3) = 3x + 2(3x + 2)
ans: x = −2
j. 2 + 3(x + 1) = x + 2(x − 1)
ans: Inconsistent, no solution.
k. −5x − 3 = x − 2(3x + 1) − 1
ans: Identity, all real numbers are solutions.
l. 4x − 2 = 10
ans: x = 3
m. 3(x − 4) − 3 = 4(x + 3) − x − 27
ans: Identity, all real numbers are solutions.
n. 4x − 2(x − 3) = 3 − 4(x + 1)
7
6
o. −8x + 2(3x − 1) = 4 − 2(x + 1)
ans: x = −
ans: Inconsistent, no solution
p. 12x − 3(x − 2) = 5x + 6
ans: x = 0
q. 3x = 12
ans: x = 4
1
r. 4x − 10 = 14
ans: x = 6
s. −12 − 3x = 2x + 3
ans: x = −3
t. 3 − 2(2x − 2) = 4x + 5
1
4
u. −2(−3x + 7) + 5 = 4x − 2(−x + 4) − 1
ans: x =
ans: Identity, all real numbers are solutions.
v. 4(−2x + 3) − 2x = −3x − 2(−x − 5)
2
9
w. 2x − 3(2 − x) − 4x = 12 − 4(2x + 1)
ans: x =
14
9
x. 3x − 7 = 12
19
ans: x =
3
y. 4 − 2(x + 1) = 5x + 2
ans: x =
ans: x = 0
z. 4(x − 2) − 3(x + 1) = x + 3
ans: Inconsistent, no solution
aa. −2(3x + 4) + 2 = 4 − 3(x − 2)
16
3
bb. 12 − 4(2x + 1) = 4(x − 2) − 3
ans: x = −
19
12
cc. 3(x − 4) − 3 = 4(x + 3) − x − 27
ans: x =
ans: Identity, all real numbers are solutions
dd. 4x − 2(x − 3) = 3 − 4(x + 1)
7
6
ee. −8x + 2(3x − 1) = 4 − 2(x + 1)
ans: x = −
ans: Inconsistent, no solution
ff. 12x − 3(x − 2) = 5x + 6
ans: x = 0
gg. 2x − 6(x − 1) = 4 + 3(x − 3)
11
7
hh. 3 − 2(x + 4) = −2x + 5
ans: x =
ans: Inconsistent, no solution
2
2. Solve the equation:
2x
4
=
5
7
10
ans: x =
7
x x
b. + = 4
2
3
24
ans: x =
5
−2x + 1 −3x + 2
2x − 1
c.
−
=
4
3
6
3
ans: x =
2
−4x + 1
2x − 5
d.
=
7
3
19
ans: x =
13
−3x − 2 2x − 1
x+1
e. −
+
=2−
5
10
10
16
ans: x =
9
−x + 3
x+1
=
−4
f. 3x −
3
5
46
ans: x = −
43
2x − 1
4
g.
= x+2
5
7
77
ans: x = −
6
x−2
−3x − 1 −2x + 2
−
=
h.
3
3
9
7
ans: x = −
4
−3x − 2
x
i. −
−3=2−
5
5
23
ans: x =
4
2
1
j. − (2x − 1) + 2x = (x − 2) + 5
3
3
ans: x = 11
3
2
k. − (x − 3) + 4x = (4x − 2) − 5
4
3
103
ans: x = −
7
3
1
1
l. x − x = (x − 3)
4
2
2
ans: x = 6
x
5
x
m. − 2( + 2) = 1 + x
3
2
6
a.
3
ans: x = −
10
3
2
2
3 3
n. 2 − ( x + 3(4 − x)) = − + 1
3
5
5 5
165
ans: x =
8
1
1
o. + x = − (x − 4)
3
3
3
ans: x =
4
1
1
p. x − 3(x + 2) = − 2(x + 1)
3
2
27
ans: x = −
4
4
3. Solve the equation:
a. 0.04x − 0.2(3x + 5) = 1.2x + 0.6
10
11
b. 1.22x + 0.5(x − 2) = 2.72x − 0.1(10x + 5)
ans: x = −
ans: Inconsistent, no solution
4. Solve the equation:
a. |3x − 5| = 16
11
3
b. 4 + | − 2x + 7| = 2
ans: x = 7 or x = −
ans: Inconsistent, no solution
5. Solve the equation for the indicated variable:
a. 2ab + x = 3y, solve for b
ans: b =
3y − x
2a
b. F = 12 m − y, solve for m
ans: m = 2F + 2y
c. P = 2L + 2W , solve for W
P − 2L
2
d. y = mx + b, solve for x
ans: W =
y−b
m
e. 3x + 3y = 6r,
ans: x =
solve for y.
ans: y = 2r − x
f. xy − 2r = 10 + r,
ans: x =
solve for x.
10 + 3r
y
5