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What is the value of [tex]\( x \)[/tex] when using algebra tiles to solve the equation [tex]\( x + 1 = -x - 5 \)[/tex]?

A. [tex]\( x = -1 \)[/tex]
B. [tex]\( x = 1 \)[/tex]
C. [tex]\( x = 2 \)[/tex]
D. [tex]\( x = -3 \)[/tex]

Sagot :

GinnyAnsweridn
To find the value of [tex]\( x \)[/tex] using algebra tiles to solve the equation [tex]\( x + 1 = -x + (-5) \)[/tex], we will proceed step-by-step.

### Step 1: Setup the Equation with Algebra Tiles
- On the left side of the equation, we have [tex]\( x + 1 \)[/tex].
- On the right side, we have [tex]\( -x + (-5) \)[/tex].

### Step 2: Combine Like Terms
The goal is to isolate the variable [tex]\( x \)[/tex]. We can start by adding [tex]\( x \)[/tex] to both sides of the equation to eliminate [tex]\( -x \)[/tex] from the right side.

So,

[tex]\[ x + x + 1 = -x + x + (-5) \][/tex]

This simplifies to:

[tex]\[ 2x + 1 = -5 \][/tex]

### Step 3: Isolate the Variable [tex]\( x \)[/tex]
Next, we need to isolate [tex]\( 2x \)[/tex]. Subtract 1 from both sides of the equation:

[tex]\[ 2x + 1 - 1 = -5 - 1 \][/tex]

This simplifies to:

[tex]\[ 2x = -6 \][/tex]

### Step 4: Solve for [tex]\( x \)[/tex]
Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:

[tex]\[ \frac{2x}{2} = \frac{-6}{2} \][/tex]

This simplifies to:

[tex]\[ x = -3 \][/tex]

### Conclusion
So, the value of [tex]\( x \)[/tex] when using algebra tiles to solve the equation [tex]\( x + 1 = -x + (-5) \)[/tex] is [tex]\(\boxed{-3}\)[/tex].

This solution matches with one of our given choices:
- [tex]\( x = -1 \)[/tex]
- [tex]\( x = 1 \)[/tex]
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = -3 \)[/tex]
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