Question

Complete each equation so that it is true for no values of x.
x - 2 = -(__- x)

Answer 1

nswer:

(x +5)^2 = -2

Step-by-step explanation: w t f

We can subtract the constant to get ...

x^2 +10x = -27

Then add the square of half the x-coefficient:

x^2 +10x +5^2 = -27 +5^2

(x +5)^2 = -2 . . . . . . write as a square

Answer 2

This equation is true for all
`\( x \)` because it simplifies to
`\( 0 = 0 \)`, meaning the value inside the box that makes the equation true is 2.

The equation presented is:

`\[ x - 2 = -(\Box - x) \]`

To solve for the value in the box
`(\( \Box \))`, we need to recognize that the expression inside the parentheses on the right side of the equation will be the opposite sign of
`\( x - 2 \)` when the negative sign outside the parentheses is distributed.

Here are the steps to find the value in the box:

1. Identify the Expression: Recognize that
`\( x - 2 \)` is the expression we are considering.

2. Apply the Negative Sign*: The negative sign outside of the parentheses will change the sign of both terms inside the parentheses.

3. Match the Expressions: The expression inside the parentheses, once negated, should match
`\( x - 2 \)`. Since distributing the negative sign across
`\( \Box - x \)` will change the sign of
`\( -x \)` to
`\( +x \)`, we want the expression
`\( \Box - x \)` to become
`\( x - 2 \)` when negated.

4. **Solve for the Box**: Knowing that the negative of
`\( \Box - x \)` should be
`\( x - 2 \)`, set
`\( -(\Box - x) = x - 2 \).`

`\[ -\Box + x = x - 2 \]`

Since
`\( x \)` is on both sides, we can simplify by removing
`\( x \)` from each side:

`\[ -\Box = -2 \]`

`\[ \Box = 2 \]`

The value in the box is 2. This means that the original equation should read:

`\[ x - 2 = -(2 - x) \]`

And when you distribute the negative sign inside the parentheses:

`\[ x - 2 = -2 + x \]`

This equation is true for all
`\( x \)` because it simplifies to
`\( 0 = 0 \)`, meaning the value inside the box that makes the equation true is 2.