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Which of the following should be done to both sides of the equation x − 3.41 = −19 to solve the value of x?

subtract 3.41
add 3.41
subtract 19
add 19

5 answers

To solve the equation \( x - 3.41 = -19 \) for \( x \), you need to isolate \( x \) on one side. You can do this by adding \( 3.41 \) to both sides of the equation.

So, the correct operation would be to:

add 3.41 to both sides of the equation.

This gives you:

\[ x - 3.41 + 3.41 = -19 + 3.41 \]

Simplifying that, you get:

\[ x = -15.59 \]

Which of the following equations has a solution of −1\2 ?
x + 1\2 = −1
x − 1/2 = 1
x + 1 = 12
x − 1 = −1/2

To find which of the equations has a solution of \(-\frac{1}{2}\), we will substitute \(-\frac{1}{2}\) for \(x\) in each equation and see if the equation holds true.

  1. \(x + \frac{1}{2} = -1\)
    \(-\frac{1}{2} + \frac{1}{2} = -1\)
    \(0 \neq -1\) (False)

  2. \(x - \frac{1}{2} = 1\)
    \(-\frac{1}{2} - \frac{1}{2} = 1\)
    \(-1 \neq 1\) (False)

  3. \(x + 1 = 12\)
    \(-\frac{1}{2} + 1 = 12\)
    \(\frac{1}{2} \neq 12\) (False)

  4. \(x - 1 = -\frac{1}{2}\)
    \(-\frac{1}{2} - 1 = -\frac{1}{2}\)
    \(-\frac{3}{2} \neq -\frac{1}{2}\) (False)

None of the equations yield a solution of \(-\frac{1}{2}\).

Let's check the calculations again:

  1. \(x + \frac{1}{2} = -1\)
    \(-\frac{1}{2} + \frac{1}{2} = 0 \neq -1\)

  2. \(x - \frac{1}{2} = 1\)
    \(-\frac{1}{2} - \frac{1}{2} = -1 \neq 1\)

  3. \(x + 1 = 12\)
    \(-\frac{1}{2} + 1 = \frac{1}{2} \neq 12\)

  4. \(x - 1 = -\frac{1}{2}\)
    \(-\frac{1}{2} - 1 = -\frac{3}{2} \neq -\frac{1}{2}\)

After re-evaluating, if any errors were in my calculations previosly, I am convinced that none of the provided equations have \(-\frac{1}{2}\) as their solution. If you have additional information or would like to present rephrased equations, please feel free to share!

so which one

Apologies for the confusion in the previous evaluation. Let's carefully check each equation again to determine which one has a solution of \(-\frac{1}{2}\).

  1. Equation: \( x + \frac{1}{2} = -1 \)
    Substituting \( x = -\frac{1}{2} \):
    \(-\frac{1}{2} + \frac{1}{2} = -1\)
    \(0 \neq -1\) (False)

  2. Equation: \( x - \frac{1}{2} = 1 \)
    Substituting \( x = -\frac{1}{2} \):
    \(-\frac{1}{2} - \frac{1}{2} = 1\)
    \(-1 \neq 1\) (False)

  3. Equation: \( x + 1 = 12 \)
    Substituting \( x = -\frac{1}{2} \):
    \(-\frac{1}{2} + 1 = 12\)
    \(\frac{1}{2} \neq 12\) (False)

  4. Equation: \( x - 1 = -\frac{1}{2} \)
    Substituting \( x = -\frac{1}{2} \):
    \(-\frac{1}{2} - 1 = -\frac{1}{2}\)
    \(-\frac{3}{2} \neq -\frac{1}{2}\) (False)

Upon reviewing these equations, it appears I mistakenly evaluated them in previous responses. Let's check the last equation more carefully:

Equation: \( x - 1 = -\frac{1}{2} \).

Adding 1 to both sides:
\( x = -\frac{1}{2} + 1 \)
\( x = \frac{1}{2} \).

The equation \( x - 1 = -\frac{1}{2} \) solved as \( x = \frac{1}{2} \) confirms that none of the equations presented has \(-\frac{1}{2}\) as a solution.

I apologize for the confusion. None of these equations have a solution of \(-\frac{1}{2}\).