Certainly! Let's solve the equation [tex]\( 3(x-4) + 5 = 2x - 2(3-x) \)[/tex] step by step, citing the appropriate algebraic property used at each step.
### Equation:
[tex]\[ 3(x-4) + 5 = 2x - 2(3-x) \][/tex]
### Step-by-Step Solution:
1. Step 1: Apply the Distributive Property.
[tex]\[
3(x-4) + 5 = 2x - 2(3-x)
\][/tex]
Using the distributive property on both sides:
[tex]\[
3x - 12 + 5 = 2x - 6 + 2x
\][/tex]
Reason: Distributive Property
2. Step 2: Combine Like Terms.
[tex]\[
3x - 12 + 5 = 2x - 6 + 2x
\][/tex]
Combine like terms on both sides:
[tex]\[
3x - 7 = 4x - 6
\][/tex]
Reason: Combining Like Terms
3. Step 3: Set the Simplified Expressions Equal to Each Other.
[tex]\[
3x - 7 = 4x - 6
\][/tex]
This is the simplified form of the equation.
Reason: Given
4. Step 4: Subtract [tex]\( 3x \)[/tex] from Both Sides to Isolate the [tex]\( x \)[/tex] Terms.
[tex]\[
3x - 7 = 4x - 6
\][/tex]
Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[
-7 = x - 6
\][/tex]
Reason: Subtraction Property of Equality
5. Step 5: Add 6 to Both Sides to Solve for [tex]\( x \)[/tex].
[tex]\[
-7 = x - 6
\][/tex]
Add 6 to both sides:
[tex]\[
-7 + 6 = x
\][/tex]
Simplify:
[tex]\[
-1 = x
\][/tex]
Reason: Addition Property of Equality
### Final Answer:
[tex]\[
x = -1
\][/tex]
By following these steps, we have solved the equation to find that [tex]\( x \)[/tex] equals [tex]\(-1\)[/tex].
