Question

clarifying big ideas: geometric proof
give the reasons for the steps used in solving the equation $3(x - 4) + 5 = 2x - 2(3 - x)$.
drag the tiles to the reason boxes. not all tiles will be used.
pairs
steps reasons
$3(x - 4) + 5 = 2x - 2(3 - x)$
$3x - 12 + 5 = 2x - 6 + 2x$
$3x - 7 = 4x - 6$
$-7 = x - 6$
$-1 = x$
tiles
combining like terms transitive property multiplication property of equality
distributive property subtraction property of equality addition property of equality
given

Explanation:

Step1: Match given equation

$3(x - 4) + 5 = 2x - 2(3 - x)$
Reason: given

Step2: Apply distributive property

$3x - 12 + 5 = 2x - 6 + 2x$
Reason: distributive property

Step3: Combine like terms

$3x - 7 = 4x - 6$
Reason: combining like terms

Step4: Subtract $3x$ from both sides

$-7 = x - 6$
Reason: subtraction property of equality

Step5: Add 6 to both sides

$-1 = x$
Reason: addition property of equality

Answer:

1. $3(x - 4) + 5 = 2x - 2(3 - x)$ → given
2. $3x - 12 + 5 = 2x - 6 + 2x$ → distributive property
3. $3x - 7 = 4x - 6$ → combining like terms
4. $-7 = x - 6$ → subtraction property of equality
5. $-1 = x$ → addition property of equality