Ask a New Question
Menu

Which of the following should be done to both sides of the equation x + 11 = −17

to solve the value of x
? (1 point).
Responses

subtract 11
subtract 11

add 17
add 17

add 11
add 11

subtract 17

11 answers

To solve the equation \( x + 11 = -17 \) for \( x \), you should subtract 11 from both sides of the equation.

This will give you:

\[ x + 11 - 11 = -17 - 11 \]

Which simplifies to:

\[ x = -28 \]

So, the correct response is subtract 11.

What is the solution of the equation x + 23 = 9
?(1 point)
Responses

14
14

−14
negative 14

32
32

−32

To solve the equation \( x + 23 = 9 \), you need to isolate \( x \). You can do this by subtracting 23 from both sides:

\[ x + 23 - 23 = 9 - 23 \]

This simplifies to:

\[ x = 9 - 23 \] \[ x = -14 \]

So, the solution of the equation is −14.

Which of the following equations has a solution of −8
?(1 point)
Responses

x − 8 = 0
x minus 8 equals 0

x − 10 = 2
x minus 10 equals 2

x − 4 = −12
x minus 4 equals negative 12

x + 3 = −11

To determine which equation has a solution of \(-8\), we can substitute \(-8\) into each equation and check if it holds true.

  1. \(x - 8 = 0\): \[ -8 - 8 = -16 \quad \text{(not true)} \]

  2. \(x - 10 = 2\): \[ -8 - 10 = -18 \quad \text{(not true)} \]

  3. \(x - 4 = -12\): \[ -8 - 4 = -12 \quad \text{(true)} \]

  4. \(x + 3 = -11\): \[ -8 + 3 = -5 \quad \text{(not true)} \]

The equation that has a solution of \(-8\) is \(x - 4 = -12\).

Which of the following should be done to both sides of the equation x − 3.41 = −19
to solve the value of x
?(1 point)
Responses

subtract 3.41
subtract 3.41

add 3.41
add 3.41

add 19
add 19

subtract 19

To solve the equation \( x - 3.41 = -19 \) for \( x \), you should add 3.41 to both sides of the equation.

This will give you:

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

Which simplifies to:

\[ x = -15.59 \]

So, the correct response is add 3.41.

Which of the following equations has a solution of −12
?(1 point)
Responses

x − 12 = 1
x minus Start Fraction 1 over 2 End Fraction equals 1

x − 1 = −12
x minus 1 equals negative Start Fraction 1 over 2 End Fraction

x + 12 = −1
x plus Start Fraction 1 over 2 End Fraction equals negative 1

x + 1 = 12
x plus 1 equals Start Fraction 1 over 2 End Fraction

To determine which equation has a solution of \(-12\), we can substitute \(-12\) into each equation and check if it holds true.

  1. \(x - 12 = 1\): \[ -12 - 12 = -24 \quad \text{(not true)} \]

  2. \(x - 1 = -12\): \[ -12 - 1 = -13 \quad \text{(not true)} \]

  3. \(x + 12 = -1\): \[ -12 + 12 = 0 \quad \text{(not true)} \]

  4. \(x + 1 = 12\): \[ -12 + 1 = -11 \quad \text{(not true)} \]

None of these equations seem to directly yield \(-12\) as a solution by substitution.

However, let's rewrite the first equation to see if one matches:

  1. \(x - 12 = 1\): \ Solving this yields: \[ x = 1 + 12 = 13 \quad \text{(not -12)} \]

  2. \(x - 1 = -12\): \ This yields: \[ x = -12 + 1 = -11 \quad \text{(not -12)} \]

  3. \(x + 12 = -1\): \ This gives: \[ x = -1 - 12 = -13 \quad \text{(not -12)} \]

  4. \(x + 1 = 12\): \ This gives: \[ x = 12 - 1 = 11 \quad \text{(not -12)} \]

It appears none of the provided equations produce \(-12\) as the solution. If there is a different set of equations I'm not seeing or misinterpreting, please verify the options or let me know!

Which of the following equations has a solution of −1/2
?(1 point)
Responses

x − 1/2 = 1
x minus Start Fraction 1 over 2 End Fraction equals 1

x − 1 = −1/2
x minus 1 equals negative Start Fraction 1 over 2 End Fraction

x + 1/2 = −1
x plus Start Fraction 1 over 2 End Fraction equals negative 1

x + 1 = 1/2
x plus 1 equals Start Fraction 1 over 2 End Fraction

To determine which equation has a solution of \(-\frac{1}{2}\), we can substitute \(-\frac{1}{2}\) into each equation and check if it holds true.

  1. \(x - \frac{1}{2} = 1\): \[ -\frac{1}{2} - \frac{1}{2} = 1 \implies -1 \neq 1 \quad \text{(not true)} \]

  2. \(x - 1 = -\frac{1}{2}\): \[ -\frac{1}{2} - 1 = -\frac{1}{2} \implies -\frac{3}{2} \neq -\frac{1}{2} \quad \text{(not true)} \]

  3. \(x + \frac{1}{2} = -1\): \[ -\frac{1}{2} + \frac{1}{2} = -1 \implies 0 \neq -1 \quad \text{(not true)} \]

  4. \(x + 1 = \frac{1}{2}\): \[ -\frac{1}{2} + 1 = \frac{1}{2} \implies \frac{1}{2} = \frac{1}{2} \quad \text{(true)} \]

The equation that has a solution of \(-\frac{1}{2}\) is \(x + 1 = \frac{1}{2}\).