Sure! Let's solve the equation [tex]\(-4x + (-3) = -x + 3\)[/tex] using algebra tiles step by step.
1. Add 4 positive [tex]\(x\)[/tex]-tiles to both sides and create zero pairs:
Initially, we have:
[tex]\[
-4x + (-3) \quad = \quad -x + 3
\][/tex]
By adding 4 positive [tex]\(x\)[/tex]-tiles to both sides of the equation, we get:
[tex]\[
-4x + 4x + (-3) \quad = \quad -x + 4x + 3
\][/tex]
This simplifies to:
[tex]\[
0 + (-3) \quad = \quad 3x + 3
\][/tex]
Which is simply:
[tex]\[
-3 \quad = \quad 3x + 3
\][/tex]
2. Add 3 negative unit tiles to both sides and create zero pairs:
Now we have:
[tex]\[
-3 \quad = \quad 3x + 3
\][/tex]
By adding 3 negative unit tiles to both sides of the equation, we get:
[tex]\[
-3 + (-3) \quad = \quad 3x + 3 + (-3)
\][/tex]
This simplifies to:
[tex]\[
-6 \quad = \quad 3x
\][/tex]
3. Divide the unit tiles evenly among the [tex]\(x\)[/tex]-tiles:
Now we have:
[tex]\[
-6 \quad = \quad 3x
\][/tex]
To isolate [tex]\(x\)[/tex], we divide both sides by the coefficient of [tex]\(x\)[/tex], which is 3:
[tex]\[
-6 \div 3 \quad = \quad 3x \div 3
\][/tex]
This results in:
[tex]\[
-2 \quad = \quad x
\][/tex]
Thus, the solution to the equation [tex]\(-4x + (-3) = -x + 3\)[/tex] is:
[tex]\[
\boxed{-2}
\][/tex]
