thegod2520
Answered

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Give the reasons for the steps used in solving the equation [tex]3(x-4)+5=2x-2(3-x)[/tex]. Drag the tiles to the reason boxes. Not all tiles will be used.

Tiles:
- addition property of equality
- distributive property
- transitive property
- subtraction property of equality
- given

Steps and Reasons:

[tex]\ \textless \ br/\ \textgreater \ \begin{array}{l}\ \textless \ br/\ \textgreater \ 3(x-4)+5=2x-2(3-x) \quad \text{(given)} \\\ \textless \ br/\ \textgreater \ 3x-12+5=2x-6+2x \quad \text{(distributive property)} \\\ \textless \ br/\ \textgreater \ 3x-7=4x-6 \quad \text{(combine like terms)} \\\ \textless \ br/\ \textgreater \ -7=x-6 \quad \text{(subtraction property of equality)} \\\ \textless \ br/\ \textgreater \ -1=x \quad \text{(combine like terms)} \\\ \textless \ br/\ \textgreater \ \end{array}\ \textless \ br/\ \textgreater \ [/tex]

Sagot :

GinnyAnswer
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]
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