Question

What is the justification for each step in the solution of the equation 13x-4=-9(4/3x)-12? Select from the drop-down menus to correctly justify each step.

1) Given
2) 13x-4=-36-27x
3) 40x-4=-24 (addition property of equality)
4) 40x=-20 (division property of equality)
5) x=-12 (division property of equality)

Answer 1

The given equation 13x - 4 = -9(4/3x) - 12 is solved using distributive property, combination of like terms, addition property of equality, and division property of equality. There is a mistake in the provided solution, as -9(4/3x) should equal -12x. After correcting the error, the proper solution is x = -0.5.

Step-by-step explanation:

Justification for Solving the Equation

Let’s take a look at the justification for each step in the solution of the equation 13x - 4 = -9(4/3x) - 12:

1. Given: The original equation is presented.
2. Distribution: Apply the distributive property to -9(4/3x) to get -36/3x which simplifies to -12x, resulting in 13x - 4 = -12x - 12.
3. Combination of Like Terms: Combine like terms by adding 12x to both sides (addition property of equality), resulting in 13x + 12x - 4 = -12.
4. Addition Property of Equality: Add 4 to both sides to isolate the variable term, getting 40x = -20.
5. Division Property of Equality: Divide both sides by 40 to solve for x, with the result being x = -1/2 or x = -0.5.

Note that in the original solution provided, there is a mistake in step 2, where -9(4/3x) should simplify to -12x, not -27x, and the final answer should be x = -0.5 instead of x = -12.

The correct sequence of justifications involves applying the distribution, addition property of equality, and finally the division property of equality in the algebraic process.