Rami is solving the equation for $x$.

$\begin{array}{c}
-6 x-1=5 \
-6 x-1 \square 1=(5 \square 1) \
-6 x=6 \
-6 x \bigcirc-6=6 \bigcirc-6 \
x=-1
\end{array}$

Which operation symbols should Rami write in the $\square$ and the $\bigcirc$?

A. $\square$ should contain +; $\bigcirc$ should contain $ imes$

B. $\square$ should contain $\div$; $\bigcirc$ should contain $\div$

C. $\square$ should contain -; $\bigcirc$ should contain $ imes$

D. $\square$ should contain -; $\bigcirc$ should contain $\div$

Question

Rami is solving the equation for $x$. 
 
$\begin{array}{c} 
-6 x-1=5 \ 
-6 x-1 \square 1=(5 \square 1) \ 
-6 x=6 \ 
-6 x \bigcirc-6=6 \bigcirc-6 \ 
x=-1 
\end{array}$ 
 
Which operation symbols should Rami write in the $\square$ and the $\bigcirc$? 
 
A. $\square$ should contain +; $\bigcirc$ should contain $	imes$ 
 
B. $\square$ should contain $\div$; $\bigcirc$ should contain $\div$ 
 
C. $\square$ should contain -; $\bigcirc$ should contain $	imes$ 
 
D. $\square$ should contain -; $\bigcirc$ should contain $\div$

GinnyAnswer · Answer

The first operation is addition, and the second operation is division. Therefore, □ should contain + and ◯ should contain ÷ . 
 Explanation 
 
 Analyzing the equation We are given an equation that Rami is solving for x , and we need to determine the operation symbols that should be written in the boxes. Let's analyze the steps Rami took. 
 
 Determining the first operation The first step is − 6 x − 1 = 5 . To get to the next step, − 6 x − 1 □ 1 = ( 5 □ 1 ) , we need to determine what operation is performed on both sides of the equation. Looking at the following step, − 6 x = 6 , we can see that 1 was added to both sides of the equation. Therefore, the □ should contain + . 
 
 Determining the second operation Now we have − 6 x = 6 . To get to the next step, − 6 x ◯ − 6 = 6 ◯ − 6 , we again need to determine what operation is performed on both sides of the equation. Looking at the final step, x = − 1 , we can see that both sides of the equation were divided by -6. Therefore, the ◯ should contain ÷ . 
 
 Conclusion Therefore, the □ should contain + and the ◯ should contain ÷ .

Examples 
 Understanding how to isolate a variable in an equation is a fundamental skill in algebra. For example, if you're trying to figure out how many hours you need to work to earn a certain amount of money, you might set up an equation where the number of hours is the variable. By using inverse operations like addition and division, just like Rami did, you can solve for the number of hours needed. This skill is also crucial in more advanced math and science courses.

Answer (1)

Related Questions in Mathematics

[Done] Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

[Done] Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

[Done] What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

[Done] The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

[Done] If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]