Question

Antonia incorrectly solves the equation −2(14−54a)=6 . Her work is shown below.

Determine which of her steps are correct based on the work in the previous step. Drag and drop Yes or No into each box to show if her math is correct for each step.

Then, drag and drop the correct solution into the box to make the statement true.

Answer 1

To solve the equation −2(14−54a)=6, distribute the -2, simplify the equation, isolate the variable, and divide both sides by 108 to solve for a.

Step-by-step explanation:

To solve the equation −2(14−54a)=6, we need to follow the correct steps:

1. Distribute the -2 to the terms inside the parenthesis: -2 * 14 + 2 * 54a = 6
2. Simplify the equation: -28 + 108a = 6
3. Add 28 to both sides to isolate the variable: 108a = 34
4. Divide both sides by 108 to solve for a: a = 34/108

Therefore, the correct solution is a = 17/54.

Answer 2

For the yes/no bit:

step 1: no

step 2: no

step 3: yes

step 4: yes

step 5: no

for the final answer bit: a = 2 3/5 (the last option)

Step-by-step explanation:

yes/no bit:

step 1 is wrong because she didn't multiply
`-(5)/(4)a` by -2

step 2 is wrong because she subtracted 1/2 instead of adding it

step 3 is correct because 6 - 1/2 = 11/2

step 4 is correct because she correctly multiplied both sides by 4

step 5 is wrong because she added 5 instead of dividing by -5.

for the final answer bit, I've attached an image below with my working out. hope this helps!