Solving Linear and Quadratic Equations

5(2x - 7) = 80

• x = 11.5

• x = 115

• x = 12

• x = 16

Answer explanation

To solve the equation, first distribute the 5: 10x - 35 = 80. Then, isolate x: 10x = 115. Finally, divide by 10 to find x = 11.5, which is the correct answer.

Tags

CCSS.7.EE.B.4A

Which equation below would give you the answer no solution?

• 3x + 3 = 3x + 3

• 3x + 3 = 6x + 6

• 3x + 3 = 3x + 2

• 3x + 3 = 0

Answer explanation

The equation 3x + 3 = 3x + 2 has no solution because the variables cancel out, leaving an untrue statement.

Tags

CCSS.8.EE.C.7A

Which equation below would give you an answer of infinite solutions (all real numbers)?

• 4x + 10 = 0

• 4x + 10 = 4x

• 4x + 10 = 4x + 8

• 4x + 10 = 4x + 10

Answer explanation

The equation 4x + 10 = 4x + 10 would result in infinite solutions because both sides are equal, meaning any real number for x would satisfy the equation.

Tags

CCSS.8.EE.C.7A

8v - 4(v + 8) = 8

• 2

• 10

• 4

• -4 

Answer explanation

To solve the equation, first distribute the -4: 8v - 4v - 32 = 8. Combine like terms: 4v - 32 = 8. Add 32 to both sides: 4v = 40. Divide by 4: v = 10. Therefore, the correct answer is 10.

Tags

CCSS.8.EE.C.7B

Find the error in the problem below
19 - 2k = 3k - 1
     +3k   +3k
19 + 1k = -1
-19           -19
k = -20

• They should have divided by 1 for the last step

• They should add 19 instead of subtracting 19

• I can not find an error

• Instead of adding 3k they should subtract 3k

Answer explanation

Instead of adding 3k, they should subtract 3k

Tags

CCSS.HSA.REI.A.1

• x=1         x=10

• x=-1        x=-10

• x=2          x=11

Answer explanation

To solve the quadratic x^2-11x+10=0, we need to find two numbers that multiply to 10 and add up to -11. The numbers are -1 and -10, so the solutions are x=1 and x=10.

Tags

CCSS.HSA-REI.B.4B

What are the solutions to the quadratic equation:

Answer explanation

The solutions to the quadratic equation x^2 - 6x + 5 = 0 are x = 5 and x = 1, making the correct answer choice x=5, x=1.

Tags

CCSS.HSA-REI.B.4B

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Answer explanation

To solve for x and y, set the two equations equal to each other: 2x + 1 = 4x - 1. Solve for x to get x = 1. Substitute x back into one of the equations to find y: y = 2(1) + 1 = 3. Therefore, the solution is (1,3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?

• x=8

• x=3

• x=11

• x=5

Answer explanation

To find the value of x, solve the system of equations by substituting y=-2x+8 into the first equation. Then, solve for x to get x=3, which is the correct choice.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 

• 1

• -1

• 3

• 4

Answer explanation

To find the y-coordinate, solve the system of equations to get y=1. Therefore, the value of the y-coordinate is 1.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6