Question

Mark incorrectly solved the inequality -4(5/2+3/2x) > 8. His work is shown. Which step shows an error based on the inequality ONLY from the previous step? Help please!!​

Answer 1

A. Step 1: -10 + 6x > 8

Explanation:

The correct way:

Step 1: Multiply both sides by
`-1` (reverse the inequality)

`\left(-4\left((5)/(2)+(3)/(2)x\right)\right)\left(-1\right)<8\left(-1\right)`

Step 2: Simplify

`4\left((5)/(2)+(3)/(2)x\right)<-8`

Step 3: Divide both sides by 4

`(4\left((5)/(2)+(3)/(2)x\right))/(4)<(-8)/(4)`

Step 4: Simplify

`(5)/(2)+(3)/(2)x<-2`

Step 5: Subtract
`(5)/(2)` from both sides

`(5)/(2)+(3)/(2)x-(5)/(2)<-2-(5)/(2)`

Step 6: Simplify

`(3)/(2)x<-(9)/(2)`

Step 7: Multiply both sides by 2

`2\cdot (3)/(2)x<2\left(-(9)/(2)\right)`

Step 8: Simplify

`3x<-9`

Step 9: Divide both sides by 3

`(3x)/(3)<(-9)/(3)`

Step 10: Simplify

`x<-3`

Answer 2

Answer : The incorrect step is, (A) step 1: -10 + 6x > 8

Step-by-step explanation :

The given expression is:

`-4((5)/(2)+(3)/(2)x)>8`

Now solving this expression step by step.

First -4 distributed over parentheses.

`(-4* (5)/(2))+(-4* (3)/(2)x)>8`

Now solving bracket term, we get:

`-10-6x>8`

Now taking like terms together, we get:

`-6x>8+10`

`-6x>18`

`-x>3`

Now multiplying this expression by (-1), we get:

`x>-3`

Thus, the incorrect step is, (A) step 1: -10 + 6x > 8