Kelia is solving an equation for x

Question

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

4 + 6x = 1
4 plus 6 x equals 1

6 + 4x = 1
6 plus 4 x equals 1

4 + x6 = 1
4 plus Start Fraction x over 6 End Fraction equals 1

6 + x4 = 1
6 plus Start Fraction x over 4 End Fraction equals 1

Answer 1

To determine which equation Kelia is solving by multiplying both sides by 4, we can analyze each option:

1. 4 + 6x = 1

   • If she multiplies both sides by 4:
     \( 4(4 + 6x) = 4(1) \)
     This leads to:
     \( 16 + 24x = 4 \)
   • This is not a step that reflects a clear intention to simplify or isolate \( x \).

2. 6 + 4x = 1

   • If she multiplies both sides by 4:
     \( 4(6 + 4x) = 4(1) \)
     Leads to:
     \( 24 + 16x = 4 \)
   • This also does not seem to represent a clear step towards isolating \( x \).

3. 4 + x/6 = 1

   • If she multiplies both sides by 4:
     \( 4(4 + x/6) = 4(1) \)
     Leads to:
     \( 16 + \frac{4x}{6} = 4 \)
     This is equivalent to:
     \( 16 + \frac{2x}{3} = 4 \)
   • This does not simplify nicely and looks convoluted with the fraction.

4. 6 + x/4 = 1

   • If she multiplies both sides by 4:
     \( 4(6 + x/4) = 4(1) \)
     Leads to:
     \( 24 + x = 4 \)
     This clearly isolates \( x \) in the subsequent steps, making it a viable option.

Given these analyses, the most likely equation that Kelia is solving, where her second step is to multiply both sides by 4, would be:

6 + x/4 = 1.