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[tex]$3(x-4)+5=2x-2(3-x)$[/tex] & Combining like terms & [tex]$3(x-4)+5=2x-2(3-x)$[/tex] \\
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[tex]$3x-12+5=2x-6+2x$[/tex] & Distributive property & [tex]$3(x-4)+5=2x-2(3-x)$[/tex] \\
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[tex]$3x-7=4x-6$[/tex] & Addition property of equality & [tex]$3x-12+5=2x-6+2x$[/tex] \\
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[tex]$-7=x-6$[/tex] & Subtraction property of equality & [tex]$3x-7=4x-6$[/tex] \\
\hline
[tex]$-1=x$[/tex] & Subtraction property of equality & [tex]$-7=x-6$[/tex] \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
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].
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