Question

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

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

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 2

- 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 3

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 4

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