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Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
The equation − 6x + 2 = 0 is equivalent to − 6x = 2.
Choose the correct answer below.
A. The statement is false. The equation − 6x + 2 = 0 is equivalent to 6x = − 2.
B. The statement is true.
C. The statement is false. The equation − 6x + 2 = 0 is equivalent to − 6x = − 2.
D. The statement is false. The equation − 6x + 2 = 0 is equivalent to 6x = 2.
Solve the following equation. Be sure to check your proposed solution by substituting it for the variable in the given equation.
3x = − 12
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is . (Type an integer or a simplified fraction.)
B. The solution set is {x x is a real number}.
C. The solution set is ∅.
Solve the following equation. Be sure to check your proposed solution by substituting it for the variable in the given equation.
4x − 17 = − 77
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is . (Type an integer or a simplified fraction.)
B. The solution set is {x x is a real number}.
C. The solution set is ∅.
Solve the equation. Be sure to check your proposed solution by substituting it for the variable in the original equation.
9(4x − 8) = 44
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is . (Type an integer or a simplified fraction.)
B. The solution set is {x x is a real number}.
C. The solution set is ∅.
Solve the linear equation.
4x + 1 = 2x + 29
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is . (Type an integer or a simplified fraction.)
B. The solution set is {x x is a real number}.
C. The solution set is ∅.

Sample Solution

The statement “The equation − 6x + 2 = 0 is equivalent to − 6x = 2” is false.

To see why, let’s subtract 2 from both sides of the equation − 6x + 2 = 0. This gives us − 6x = −2. However, if we divide both sides of this equation by −6, we get 6x = 2, which is not the same as − 6x = 2.

Therefore, the statement is false. The correct statement would be: “The equation − 6x + 2 = 0 is equivalent to 6x = − 2”.

Solution to 3x = − 12

To solve this equation, we can divide both sides by 3. This gives us x = − 4.

To check our solution, we can substitute − 4 for x in the original equation. This gives us 3(− 4) = − 12, which is true.

Therefore, the solution set is {−4}.

Solution to 4x − 17 = − 77

To solve this equation, we can add 17 to both sides. This gives us 4x = − 60.

To solve for x, we can divide both sides by 4. This gives us x = − 15.

To check our solution, we can substitute − 15 for x in the original equation. This gives us 4(− 15) − 17 = − 60 − 17, which is true.

Therefore, the solution set is {−15}.

Solution to 9(4x − 8) = 44

To solve this equation, we can distribute the 9 on the left-hand side. This gives us 36x − 72 = 44.

We can then add 72 to both sides to get 36x = 116.

To solve for x, we can divide both sides by 36. This gives us x = 3.

To check our solution, we can substitute 3 for x in the original equation. This gives us 9(4(3) − 8) = 9(12 − 8) = 9(4) = 36, which is true.

Therefore, the solution set is {3}.

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