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

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

Step-by-step explanation :

The given expression is:

$-4(\frac{5}{2}+\frac{3}{2}x)>8$

Now solving this expression step by step.

First -4 distributed over parentheses.

$(-4\times \frac{5}{2})+(-4\times \frac{3}{2}x)>8$

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

Answer 2

Answer:

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

Step-by-step explanation:

The correct way:

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

$\left(-4\left(\frac{5}{2}+\frac{3}{2}x\right)\right)\left(-1\right)<8\left(-1\right)$

Step 2: Simplify

$4\left(\frac{5}{2}+\frac{3}{2}x\right)<-8$

Step 3: Divide both sides by 4

$\frac{4\left(\frac{5}{2}+\frac{3}{2}x\right)}{4}<\frac{-8}{4}$

Step 4: Simplify

$\frac{5}{2}+\frac{3}{2}x<-2$

Step 5: Subtract $\frac{5}{2}$ from both sides

$\frac{5}{2}+\frac{3}{2}x-\frac{5}{2}<-2-\frac{5}{2}$

Step 6: Simplify

$\frac{3}{2}x<-\frac{9}{2}$

Step 7: Multiply both sides by 2

$2\cdot \frac{3}{2}x<2\left(-\frac{9}{2}\right)$

Step 8: Simplify

$3x<-9$

Step 9: Divide both sides by 3

$\frac{3x}{3}<\frac{-9}{3}$

Step 10: Simplify

$x<-3$