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Solve each equation.
1.
 2 x  5  7  (x  3)
3
2x  5  7  x  3
3
2x  5  4  x
3
+5
Algebra 2
Extra #1.6 Review
Solving Equations
{take out parentheses}
{combine like terms}
+5
2x  9  x
3
+x
3
+x
1x  9
3
{multiply both sides by 3}
x = 27
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2. -(x + 2) – 2x = -2(x + 1)
-x – 2 – 2x = -2x – 2 {take out parentheses, distributive property}
-3x – 2 = -2x – 2 {combine like terms}
+2
+2
-3x = -2x + 0
+2x
+2x
-x = 0
x=0
{divide both sides by -1}
3. 4(-3x + 1) = -10(x – 4) – 14x
-12x + 4 = -10x + 40 – 14x {distributive property}
-12x + 4 = -24x + 40 {combine like terms}
-4
-4
-12x = -24x + 36
+24x
+24x
12x = 36
x=3
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4.
7 x  1  2x  5
2 +1
+1
7 x  2x  6
2
-2x
-2x
3x  6
2
x=4
{multiply both sides by 2/3}
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5.
nn  2
30
2 5
3
15
{multiply by least common
denominator to clear fractions}
6   10  

n

30   30  n   30  2 


 3
2 
5
 





15n + 6n = 20
21n = 20
n  20
21
{multiply each term by
common denominator}
{cancel and multiply}
{combine like terms}
{divide both sides by 21}
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6. x2 – 15 = 2x
-2x
-2x
x2 – 2x – 15 = 0 {get everything to one side in “standard form”}
(x – 5)(x + 3) = 0 {factor into two binomials}
x – 5 = 0 or x + 3 = 0 {set each factor equal to 0}
+5 +5
-3
-3
x = 5 or x = -3
7. -10n = n2 + 25
+10n
+10n
n2 + 10n + 25 = 0
(n + 5)(n + 5) = 0
n+5=0
{get everything to one side in “standard form”}
{factor into two binomials}
{set each factor (the same) equal to 0}
-5 -5
n = -5
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8. z2 = 49
z = 7 or -7
{take the square root of both sides}
9. x2 + 18x + 70 = -11
+11
+11
x2 + 18x + 81 = 0
(x + 9)(x + 9) = 0
x+9=0
{get everything to one side “standard form”}
{factor into two binomials}
{set each factor (the same) equal to 0}
-9 -9
x = -9
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10. 2x2 – 4x – 30 = 0
2(x2 – 2x – 15) = 0 {factor 2 out}
2(x – 5)(x + 3) = 0 {factor parentheses into 2 binomials}
x – 5 = 0 or x + 3 = 0 {set each factor equal to 0; not the 2, it can’t equal 0}
+5 +5
-3
-3
x = 5 or x = -3
11. 2w2 – 5w = 3
-3
-3
2w2 – 5w – 3 = 0
(2w + 1)(w – 3) = 0 {factor into 2 binomials}
2w + 1 = 0 or w – 3 = 0 {set each factor equal to 0}
-1 -1
2w = -1
+3 +3
w=3
w = -½ or
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12.
Solve : S  B  1 PS, for P
2
-B
-B
S  B  1 PS
2
S  B  1P
S
2
P  2(S  B)
S
{divide both sides by S}
{multiply both sides by 2}
© Mr. Sims
Solve each equation.
1.) 4x + 3(x – 2) = 18 – x
2.) 15 – 2x = -4(x + 1) + 9
3.) 1 (b  10)  7  1 (b  9)
5
3
4.)
5.) z2 – 10z = -21
6.) Solve: V = LWH, for W
Algebra 2
Extra #1.6
Assignment
4
8
(n  10)  
5
9
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