Question 1

Graph the inequality on a number line. x > -1

Accepted Answer

The answer of Graph the inequality on a number line....

Question 2

Solve. 5 - 4(3x - 2) = 2 + 3(2x - 5)

Accepted Answer

A

Question 3

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. -(9x - 18) + 6x = 20 - 2(x + 1)

Accepted Answer

Simplifying the equation, we get:

-9x + 18 + 6x = 20 - 2x - 2

-x + 18 = 18 - 2x

Adding 2x to both sides, we get:

x + 18 = 18

Subtracting 18 from both sides, we get:

x = 0

Therefore, the equation is conditional, and the solution is x = 0.

Question 4

The following equation is given in ax + b = c form. Solve by identifying the value of a, b, and c, then using the formula  . 3x - 4 = -34

Accepted Answer

The given equation is 3x - 4 = -34, which can be rewritten as 3x = -34 + 4 or 3x = -30.
Identifying the values, we have a = 3, b = -4, and c = -34.
Using the formula x = (c - b) / a, we get x = (-34 - (-4)) / 3 or x = -30 / 3 or x = -10.
Therefore, the correct choice is B: a = 3; b = -4; c = -34; x = -10.

Question 5

At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 35 mph. At 11:00 a.m., a second truck leaves along the same route, traveling at 70 mph. When will the second truck catch up to the first?

Accepted Answer

The first truck has a 2-hour head start, traveling 70 miles (35 mph * 2 hours) before the second truck starts. The second truck closes the gap at a rate of 35 mph (70 mph - 35 mph). To cover the 70-mile gap at 35 mph takes 2 hours, so the second truck catches up at 1:00 p.m.

Question 6

Solve for y. 3x - 2y = 6

Accepted Answer

The answer of Solve for y. 3x - 2y =...

Question 7

How much pure antifreeze must be added to 12 gallons of 20% antifreeze to make a 40% antifreeze solution?

Accepted Answer

Let X be the amount of pure antifreeze needed to be added.

Initial antifreeze amount = 20% of 12 gallons = 2.4 gallons

Final antifreeze amount = 40% of (12+X) gallons

Using the formula for concentration, we can equate the two:

2.4 + X = 0.4(12+X)

Solving for X gives us X=4 gallons. Therefore, we need to add 4 gallons of pure antifreeze to make a 40% antifreeze solution.

Question 8

Solve for y.

Accepted Answer

The answer of Solve for y. ...

Question 9

Identify the equation as linear or nonlinear. If nonlinear, state why. Do not solve.

Accepted Answer

The answer of Identify the equation as linear or nonlinear....

Question 10

Solve. 0.2(5 - 2.4x) - 3.4 = 0

Accepted Answer

The answer of Solve. 0.2(5 - 2.4x) - 3.4 =...

Question 11

Solve. 16 = 32 -

Accepted Answer

The given equation can be simplified as:

16 = 32 - 11ea7f29_4f9c_e3d5_9ecd_6986a5ee4e98_TB3307_11

Now, we need to find the value of ea7f29_4f9c_e3d5_9ecd_6986a5ee4e98_TB3307_11.

Since we don't have any information about this value, we can't solve for it.

Hence, the answer is C (14) since we can't determine the value of the variable.

Question 12

Give the total amount of the mix that results and the worth per pound of the mix when 8 pounds of nuts worth $1.20 per pound are mixed with 8 pounds of nuts worth $4.20 per pound.

Accepted Answer

The answer of Give the total amount of the mix...

Question 13

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution.
-4(x - 3) + 5x = x + 12

Accepted Answer

The answer of Identify the equation as an identity, a...

Question 14

Solve for b. a = bc²

Accepted Answer

The answer of Solve for b. a = bc² ...

Question 15

Solve for y. w = xyz

Accepted Answer

The answer of Solve for y. w = xyz...

Question 16

A consultant traveled 450 miles to attend a meeting, traveling 50 mph hours for the first part of the trip, then increasing to a speed of 60 mph for the second part. If the entire trip took 8 hours, how far did the consultant travel at the faster speed?

Accepted Answer

The answer of A consultant traveled 450 miles to attend...

Question 17

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution.
-6(x + 3) = -3 + 3(-2x - 5)

Accepted Answer

The answer of Identify the equation as an identity, a...

Question 18

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. 2x + 10(-x - 7) = -54 - 4(2x + 3)

Accepted Answer

The answer of Identify the equation as an identity, a...

Question 19

Find two consecutive even integers such that the sum of the smaller integer plus twice the larger integer is 148.

Accepted Answer

The answer of Find two consecutive even integers such that...

Question 20

Solve.  - 5 =  - 1

Accepted Answer

The answer of Solve.  - 5 =  -...

Quiz 1: Equations and Inequalities

Graph the inequality on a number line. x > -1

Solve. 5 - 4(3x - 2) = 2 + 3(2x - 5)

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. -(9x - 18) + 6x = 20 - 2(x + 1)

The following equation is given in ax + b = c form. Solve by identifying the value of a, b, and c, then using the formula . 3x - 4 = -34

At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 35 mph. At 11:00 a.m., a second truck leaves along the same route, traveling at 70 mph. When will the second truck catch up to the first?

Solve for y. 3x - 2y = 6

How much pure antifreeze must be added to 12 gallons of 20% antifreeze to make a 40% antifreeze solution?

Solve for y.

Identify the equation as linear or nonlinear. If nonlinear, state why. Do not solve.

Solve. 0.2(5 - 2.4x) - 3.4 = 0

Solve. 16 = 32 -

Give the total amount of the mix that results and the worth per pound of the mix when 8 pounds of nuts worth $1.20 per pound are mixed with 8 pounds of nuts worth $4.20 per pound.

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. -4(x - 3) + 5x = x + 12

Solve for b. a = bc2

Solve for y. w = xyz

A consultant traveled 450 miles to attend a meeting, traveling 50 mph hours for the first part of the trip, then increasing to a speed of 60 mph for the second part. If the entire trip took 8 hours, how far did the consultant travel at the faster speed?

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. -6(x + 3) = -3 + 3(-2x - 5)

Identify the equation as an identity, a contradiction, or a conditional equation. If conditional, state the solution. 2x + 10(-x - 7) = -54 - 4(2x + 3)

Find two consecutive even integers such that the sum of the smaller integer plus twice the larger integer is 148.

Solve. - 5 = - 1

Solve for b. a = bc²