Decreasing half of a number by 19.7 results in –4.1. What is the number?

Question

Use the given equation to find the number.

One-halfx – 19.7 = –4.1



What is the number?

7.8
15.6
31.2

Answer 1

To find the number \( x \), we start with the equation given:

\[ \frac{1}{2}x - 19.7 = -4.1 \]

First, we will isolate \( \frac{1}{2}x \) by adding 19.7 to both sides of the equation:

\[ \frac{1}{2}x = -4.1 + 19.7 \]

Calculating the right side:

\[ -4.1 + 19.7 = 15.6 \]

Now, plugging this back into the equation gives us:

\[ \frac{1}{2}x = 15.6 \]

Next, to solve for \( x \), we multiply both sides by 2:

\[ x = 2 \times 15.6 \]

Calculating this results in:

\[ x = 31.2 \]

Thus, the number is:

\[ \boxed{31.2} \]

Answer 2

add 19.7 then times 2 and 31.2!! THANK YOU

The image shows a mathematical problem that requires plotting the solution set of the absolute value equation \(|-x| = 3.5\) on a number line. The number line is marked with integers from -5 to 5. This problem involves understanding how absolute values work and how to represent their solutions graphically.

Answer 3

To solve the absolute value equation \( |-x| = 3.5 \), we start by recognizing that the expression \( |-x| \) can be rewritten as \( |x| \) because the absolute value of a number is always non-negative regardless of the sign in front of it.

So, we have:

\[ |x| = 3.5 \]

The general rule for absolute value equations is that \( |a| = b \) has two solutions, \( a = b \) and \( a = -b \). Thus, we can create the equations:

1. \( x = 3.5 \)
2. \( x = -3.5 \)

Now we have two solutions: \( x = 3.5 \) and \( x = -3.5 \).

Plotting on a Number Line:

To represent these solutions on a number line that is marked with integers from -5 to 5, proceed as follows:

1. Locate the points \( 3.5 \) and \( -3.5 \) on the number line:

   • \( 3.5 \) is halfway between \( 3 \) and \( 4 \).
   • \( -3.5 \) is halfway between \( -4 \) and \( -3 \).

2. Mark these two points clearly on the number line with dots or circles.

Final Representation:

• You will have two points marked:
  • A dot or circle at \( 3.5 \)
  • A dot or circle at \( -3.5 \)

This graphical representation indicates the solution set to the equation \( |-x| = 3.5 \) on your specified number line.

Answer 4

- You will have two points marked:
- A dot or circle at \( 3.5 \)
- A dot or circle at \( -3.5 \)
{–3.5, 3.5}

TY!!

Which equations have no solution? Check all that apply.

– |x| = 0
|x| = –15
– |x| = 12
– |–x| = 9
– |–x| = –2

Answer 5

To determine which equations have no solution, we need to analyze each equation involving absolute values and the properties of non-negative values. Remember that the absolute value of any expression is always non-negative (i.e., \( |x| \geq 0 \)).

Let's evaluate each equation:

1. \(- |x| = 0\)

   • This implies \( |x| = 0 \).
   • The only solution is \( x = 0 \).
   • Solution exists.

2. \(|x| = -15\)

   • The absolute value cannot be negative.
   • There are no solutions for this equation.
   • No solution.

3. \(- |x| = 12\)

   • This implies \( |x| = -12 \).
   • The absolute value cannot be negative.
   • There are no solutions for this equation.
   • No solution.

4. \(- |–x| = 9\)

   • This implies \( |–x| = -9 \).
   • The absolute value cannot be negative.
   • There are no solutions for this equation.
   • No solution.

5. \(- |–x| = –2\)

   • This implies \( |–x| = 2 \).
   • This has solutions \( x = 2 \) and \( x = -2 \).
   • Solution exists.

Summary of equations with no solutions:

• \(|x| = -15\)
• \(- |x| = 12\)
• \(- |–x| = 9\)

So the equations that have no solution are:

• \(|x| = -15\)
• \(- |x| = 12\)
• \(- |–x| = 9\)

Therefore, the final answers are:

• \(|x| = -15\)
• \(- |x| = 12\)
• \(- |–x| = 9\)