Algebra Practice
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Basics
Exp Log
Radical eqs
Quadratic eqs
Simultaneous eqs
Basics
1. ax+b=d-e Solve for a.
a = (d-e+b)/x
a = (d-e-b)x
a = (d-e-b)/x
2. ax+bd=5e Solve for d.
d = (5e-ax)/b
d = (5e+ax)/b
d = (5e-ax)b
3. A=B/C Solve for C.
C = A/B
C = B/A
C = AB
4. B=CA Solve for A.
A = B/C
A = C/B
A = BC
5. A+B=C-D Solve for D.
D = -A-B-C
D = A+B-C
D = -A-B+C
6. A/B=C/D-E Solve for A.
A = (C/D-E)/B
A = BC/D-E
A = B(C/D-E)
7. (A/B+C)D=F Solve for A.
A = (F/D-C)B
A = FD-BC
A = F/D-BC
8. 7x+4=-4 Solve for x.
0
-8/7
8/7
9. 0=-4+x/3 Solve for x.
-4/3
12
-12
10. 8=6+5/x Solve for x.
2/5
10
5/2
11. 7=5/(x-6) Solve for x.
47/7
-37/7
-42/5
12. v=ekT/m Solve for T.
T = vm/(ek)
T = ekv/m
T = m/(ekv)
13. v=ekT/m Solve for m.
m = vT/(ek)
m = ekT/v
m = T/(ekv)
14. 12=-4(-6x-3) Solve for x.
-1
1
0
15. -3(2-3x)-4(7-2x)=6x-x Solve for x.
17/6
-34/12
34/21
16. f=xy Solve for x.
x = y/f
x = f/y
x = fy
17. T=Y(1+u/g) Solve for Y.
Y = T(1+u/g)
Y = (1+u/g)/T
Y = T/(1+u/g)
Exponent and Logarithm
1. Calculate x
3
x
8
.
x
5
x
11
x
24
2. Calculate x
7
x
-4
.
x
11
x
-3
x
3
3. Calculate x
2
x
-1
x.
x
2
x
1
x
-1
4. Calculate x
4
x
-2
/x
3
.
x
5
x
-1
x
3
5. Calculate x
-2
x
-2
/x
-4
.
1
0
x
-8
6. e
x
-2=0 Solve for x.
2
ln2
2/e
7. ln[x(3x-7)]
3
Expand this.
3[lnx+ln(3x-7)]
3lnx+ln(3x-7)
lnx+3ln(3x-7)
Radical equations
1.
√
x + 1
=4 Solve for x
.
8
15
1
2. √
a
2
+
b
2
=5 Solve for b.
b = √
a
2
+
5
2
b = √
a
2
-
25
b = √
a
2
+
5
2
3. √
2
2
+
a
2
+3=8 Solve for a.
a = √
21
a = √
29
a = √
9
4. √
x
2
+
7
-9=2 Solve for x.
x = √
121
x = √
128
x = √
114
5. √
4
2
+
7
-x=3 Solve for x.
x = √
23
+3
x = √
23
-3
x = -√
23
+3
Quadratic equations
1. 4x
2
-9=0 Solve for x.
9/4
±36
±√(9/4)
2. 2x
2
-x=0 Solve for x.
0
0, 0.5
0, √0.5
3. x
2
+2x-8=0 Solve for x.
2, -4
-2, 4
-2, -4
4. x
2
+6x+9=0 Solve for x.
3
-3
0, -3
Simultaneous equations
1. 4x+6y=8
2x-5y=9 Solve for x and y.
x=16/47, y=5/8
x=-47/16, y=5/8
x=47/16, y=-5/8
2. x+6y=5
2x+2y=20 Solve for x and y.
x=1, y=11
x=11, y=-1
x=-11, y=1
3. 8x+12y=100
4x+242y=14 Solve for x and y.
x=-2, y=15.5
x=15.5, y=2
x=15.5, y=2
4. 10x+2y=4
5x+6y=6 Solve for x and y.
x=0.24, y=0.8
x=-0.8, y=-0.24
x=-0.24, y=0.8
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