Solve the equation 5(a − 7) + 11 = 2a − 3(a + 4) for a.

A. a = 0.75
Incorrect. Don’t forget to distribute to both quantities inside the parentheses.

B. a = 2
Correct! After distributing like terms were collected and the value for a was found.

C. a = -9
Incorrect. Don’t forget to add the opposite when moving a term to the other side of the equation.

D. a = 1.5
Incorrect. You will need to distribute and use inverse operations to solve for a.

Which of the following is equivalent to 5x + 8y ≤ 20?

1. y ≥ - 8 5x + 8 20
2. y ≤ - 8 5x + 8 20
3. y ≥ - 5 8x + 20 8
4. y ≤ - 5 8x + 20 8

A.
Incorrect. You made a sign error.

B.
Correct!

C.
Incorrect. Check your solution for the binomial 3x + 4 = 0.

D.
Incorrect. Check your solution for the binomial x – 3 = 0.

If (x, 3.4) is a solution to the equation 3x – 5y = 55, what is the value of x?

A. x = 24
Correct! First the y value, 3.4, was substituted into the equation and then the value of x was found.

B. x = 12.7
Incorrect. Be sure to add the opposite when moving one term across the equal sign.

C. x = 20.7
Incorrect. Check your addition.

D. x = 11
Incorrect. Substitute the known value of y, then use inverse operations to determine the value of x.

Which of the following is equivalent to 2x − 3y ≥ 12?

1. y ≥ - 2 3x − 4
2. y ≤ -  2 3x − 4
3. y ≤ - 3 2x − 6
4. y ≤ - 2 3x + 4

A.
Incorrect. You probably forgot to reverse the inequality sign when you divided both sides of the inequality by -3.

B.
Correct! After adding -2x to both sides the sign was reversed when the inequality was divided by a -3.

C.
Incorrect. You should have divided by -3 instead of -2.

D.
Incorrect. You probably made a sign error when you divided by -3.