Math
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}.