Question

A student is solving the equation 10x−3+2x=6(x−3). Which describes a first step the student could use to solve the equation correctly?
The student can combine like terms on the left side of the equation, resulting in 9x=6(x−3).

The student can combine like terms on the left side of the equation, resulting in 9 x = 6 ( x − − 3 ) .

The student can combine like terms on the left side of the equation, resulting in 12x−3=6(x−3).

The student can combine like terms on the left side of the equation, resulting in 12 x − − 3 = 6 ( x − − 3 ) .

The student can distribute 6 on the right side of the equation, resulting in 10x−3+2x=6x−3.

The student can distribute 6 on the right side of the equation, resulting in 10 x − − 3 + 2 x = 6 x − − 3 .

The student can distribute 6 on the right side of the equation, resulting in 10x−3+2x=6x+18.

The student can distribute 6 on the right side of the equation, resulting in 10 x − − 3 + 2 x = 6 x + 18 .

Answer 1

Students can combine like terms on the left side of the equation, resulting in 12x−3=6(x−3).

Given the equation solved by a student

10x−3+2x=6(x−3)

• The first step that the student could use to solve the expression correctly is to expand the bracket on the right-hand side of the equation using the distributive law as shown:

$10x-3+2x=6(x-3)\\10x-3+2x=6x - 6(3)\\10x-3+2x=6x - 18$

• The student can also combine like terms on the left side of the equation, to give;

$10x-3+2x=6(x-3). \\10x+2x-3=6(x-3)\\12x-3=6(x-3)$

Hence the correct option will be students can combine like terms on the left side of the equation, resulting in 12x−3=6(x−3).

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