Question

Answer two questions about Equations AAA and BBB: \begin{aligned} A.&&\dfrac x4+1&=-3 \\\\ B.&&x+4&=-12 \end{aligned} A. B. ​ ​ 4 x ​ +1 x+4 ​ =−3 =−12 ​ 1) How can we get Equation BBB from Equation AAA? Choose 1 answer: Choose 1 answer: (Choice A) A Rewrite one side (or both) using the distributive property (Choice B) B Rewrite one side (or both) by combining like terms (Choice C) C Multiply/divide only one side by a non-zero constant (Choice D) D Multiply/divide both sides by the same non-zero constant 2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution? Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No

Answer 1

The given equations are as follows

$\begin{aligned} A.&&\dfrac x4+1&=-3 \\\\ B.&&x+4&=-12 \end{aligned}$

(1) First, multiply both sides of equation A by 4, we have

$4\times\left(\frac{x}{4} +1\right)=4\times(-3)$

Then, rewrite the left-hand side of the above equation by using the distributive property, we have

$4\times\frac{x}{4}+4\times1=4(-3)$

$\Rightarrow x+4=-12$

This is the required equation B.

In this way, first use choice D: Multiply both sides by the same non-zero constant, i.e 4.

Then, apply choice A to solve the equation, i.e using the distributive property to solve the left-hand side of the equation.

(2) In the previous answer, equation B has been derived from equation A, hence, both the equations are equivalent.

As both the equations are the same, so both will have the same solution.

Yes, they have the same solution.