Certainly! Let's match the steps in solving the equation [tex]\(3(x-4)+5=2x-2(3-x)\)[/tex] with the appropriate reasons.
Steps:
1. [tex]\(3(x-4)+5 = 2x-2(3-x)\)[/tex]
2. [tex]\(3x-12+5 = 2x-6+2x\)[/tex]
3. [tex]\(3x-7 = 4x-6\)[/tex]
4. [tex]\(-7 = x-6\)[/tex]
5. [tex]\(x = -1\)[/tex]
Reasons:
1. given
2. distributive property
3. combine like terms
4. subtraction property of equality
5. addition property of equality
Putting them together:
[tex]\[
\begin{array}{ll}
3(x-4)+5=2 x-2(3-x) & \quad \text{given} \\
3 x-12+5=2 x-6+2 x & \quad \text{distributive property} \\
3 x-7=4 x-6 & \quad \text{combine like terms} \\
-7=x-6 & \quad \text{subtraction property of equality} \\
x = - 1 & \quad \text{addition property of equality} \\
\end{array}
\][/tex]
Therefore, the correctly matched steps and reasons are:
1. [tex]\( 3(x-4)+5=2x-2(3-x) \quad \longrightarrow \)[/tex] [tex]\( \text{given} \)[/tex]
2. [tex]\( 3x-12+5=2x-6+2x \quad \longrightarrow \)[/tex] [tex]\( \text{distributive property} \)[/tex]
3. [tex]\( 3x-7=4x-6 \quad \longrightarrow \)[/tex] [tex]\( \text{combine like terms} \)[/tex]
4. [tex]\( -7=x-6 \quad \longrightarrow \)[/tex] [tex]\( \text{subtraction property of equality} \)[/tex]
5. [tex]\( x = -1 \quad \longrightarrow \)[/tex] [tex]\( \text{addition property of equality} \)[/tex]
