Kelia is solving an equation for x

Question

𝑥
. Her second step is to multiply both sides of the equation by 4. Which equation is she solving?(1 point)
Responses

6 + 4x = 1
6

+

4
𝑥

=

1
6 plus 4 x equals 1

6 + x4 = 1
6

+

𝑥
4

=

1
6 plus Start Fraction x over 4 End Fraction equals 1

4 + x6 = 1
4

+

𝑥
6

=

1
4 plus Start Fraction x over 6 End Fraction equals 1

4 + 6x = 1

Answer 1

To determine which equation Kelia is solving based on her multiplying both sides by 4, we need to think about the step she is taking and how it aligns with common algebraic manipulations.

• If she is multiplying both sides of an equation by 4, the original equation before this step must have had a fraction where multiplying by 4 eliminates that fraction.

Let's analyze the options given:

1. 6 + 4x = 1

   • Multiplying both sides by 4 does not make sense as it will change the equation significantly.

2. 6 + x/4 = 1

   • If she had this equation and multiplied both sides by 4, we would get: \[ 4(6 + x/4) = 4(1) \implies 24 + x = 4 \]
   • This works because multiplying clearly affects the fraction.

3. 4 + x/6 = 1

   • If she had this equation and multiplied both sides by 4, we would get: \[ 4(4 + x/6) = 4(1) \implies 16 + \frac{2}{3}x = 4 \]
   • This also works but does not match the common format.

4. 4 + 6x = 1

   • Similar to the first option, multiplying here would not logically continue the problem.

From the analysis, the second option \(6 + \frac{x}{4} = 1\) makes the most sense as it allows for multiplying both sides by 4 to eliminate the fraction. Therefore, the correct equation Kelia is solving is:

6 + x/4 = 1