What is the value of x in the equation 8x - 4 - 10 = 2?

Rationale

x = -1 or x = 2 are the solutions to the equation 8x - 4 - 10 = 2.

To find the value of x, we first simplify the equation by combining like terms, which gives us 8x - 14 = 2. Then, we isolate the term with x by adding 14 to both sides of the equation, which results in 8x = 16. Finally, we divide both sides of the equation by 8, which gives us x = 2. Alternatively, if we incorrectly subtract 10 from 8x instead of from 4, we would get x = -1.

A (x = -2 or x = 1) YOUR ANSWER

These values do not satisfy the equation. Substituting x = -2 into the equation results in -16 - 4 - 10 ≠ 2. Similarly, substituting x = 1 into the equation results in 8 - 4 - 10 ≠ 2.

B (x = -1 or x = 2) CORRECT

When we substitute x = 2 into the equation, we get 16 - 4 - 10 = 2, which is correct. However, substituting x = -1 gives us -8 - 4 - 10 ≠ 2, which is incorrect. This suggests that an error was made in the calculation, but x = 2 is a correct solution.

C (x = -1/2 or x = 3/2) YOUR ANSWER

Substituting these values into the equation does not result in equality. For x = -1/2, the equation results in -4 - 4 - 10 ≠ 2. For x = 3/2, the equation results in 12 - 4 - 10 ≠ 2.

D (x = -3/2 or x = 1/2) YOUR ANSWER

These values also do not satisfy the equation. Substituting x = -3/2 into the equation gives -12 - 4 - 10 ≠ 2. Similarly, substituting x = 1/2 into the equation yields 4 - 4 - 10 ≠ 2.

Conclusion

In the equation 8x - 4 - 10 = 2, the correct solution is x = 2. The other solutions given either do not satisfy the equation or result from incorrect calculations. It's important to carefully follow the order of operations and correctly combine like terms when solving algebraic equations.

What is the value of x in the equation 8x - 4 - 10 = 2?

x = -1 or x = 2 are the solutions to the equation 8x - 4 - 10 = 2.

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