College Algebra Exercises Section 1.2
As you study these exercises, move your cursor over arrows, equal symbols, light bulbs, and highlighted words. Always check in with the wise old owl and his little apprentice by moving your cursor over them. Study with an active cursor.
| The definition that pops up when you move the cursor over a highlighted word is what should pop into your mind when you read, hear, or speak that word. | The material that pops up when you move the cursor over a light bulb is a suggested strategy for solving the problem. You should always formulate a similar strategy when you attempt to solve a problem. | When you move the cursor over an explanation of a step in a solution, the property that pops up is the mathematical justification for taking that action. You must always be able to provide such a justification for every step you take in mathematics. |
1a.
Determine if 0 is a
solution
of the equation 5x - 3 = 3x + 5
Solution:
5(0) - 3 = 3(0) + 5 is False. Therefore 0 is not a solution of the equation.
1c.
Determine if 4 is a
solution
of the equation 5x - 3 = 3x + 5
Solution:
5(4) - 3 = 3(4) + 5
17
= 17 is True. Therefore 4 is a solution of the equation.
3a.
Determine if -3 is a
solution
of the equation 3x2 + 2x - 5 = 2x2 - 2
Solution:
3(-3)2 + 2(-3) - 5 = 2(-3)2 - 2
27
- 6 - 5 = 18 - 2
16
= 16 is True. Therefore -3 is a solution of the equation.
11. Determine if 3(x + 2) = 5x + 4 is a identity or a conditional equation
Solution:
If x is replaced with 0, we obtain 3(3) = 4 which is false
Therefore 3(x + 2) = 5x + 4 is not an identity and consequently is a conditional equation.
18. Determine if x2 + 2(3x - 2) = x2 + 6x - 4 is a identity or a conditional equation
Solution:
If the distributive law is used to remove parenthesis on the left side of the equation we obtain the
equivalent equation
x2 + 6x - 4) = x2 + 6x - 4
Because the expressions on the two sides of this equation are identical it is clear that every real number is a solution. Because this equation is equivalent to the original equation, it follows that every real number is a solution of the original equation and therefore the original equation is an identity.
24. Solve the equation 7 - x =19
Solution:
Begin with the given equation
7 - x = 19 then add -7 to both sides of the equation to obtain
-x = 12. Multiply both sides of this equation by -1 to obtain
x = -12
The
solution_set
of all these equations is {-12}.
26. Solve the equation 7x + 2= 23
Solution:
Begin with the given equation
7x + 2 = 23 then add -2 to both sides of the equation to obtain
7x = 21. Multiply both sides of this equation by 
to obtain
x = 3
The
solution_set
of all these equations is {3}.
Solution:
Begin with the given equation
then multiply both sides by 10 to obtain
2x -5x = 30 + 3x. Add -3x to both sides of the equation to obtain
2x -5x - 3x = 30. Now do the indicated additions to obtain the equation
-6x = 30 and then finally multiply both sides of the equation by 
to obtain the simplest equation
x = 5
The
solution_set
of all these equations is {5}.
50. Find
the
x-intercept
and the
y-intercept
of the
graph
of the
equation
y = 16 - 3x
Solution: If y = 0,
then y = 16 - 3x
becomes
0 = 16 - 3x
. Now add 3x to both sides of the equation to obtain
3x = 16. Now multiply both sides of the equation by 
to obtain
x = 
The x-intercept of the graph of y = 16 - 3x is .
If x = 0, then y = 16 - 3x becomes y = 16 and clearly
The y-intercept of the graph of y = 16 - 3x is 16.
54. Find
the
x-intercept
and the
y-intercept
of the
graph
of the
equation
4x - 5y = 12
Solution: If y = 0,
then 4x - 5y = 12
becomes
4x
=
12
. Now multiply both sides of the equation by 
to obtain
x = 3
The x-intercept of the graph of 4x - 5y = 12 is 3.
If x = 0, then 4x - 5y = 12 becomes
-5y = 12.
Now multiply both sides of the equation by 
to obtain
y
= 
The y-intercept of the graph of 4x - 5y = 12 is 
.