Question

Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x?

Answer 1

Answer:

The first step is distributive property. The solution of the given inequality is x<-0.2.

Step-by-step explanation:

The given inequality is

$-4(2x-1)>5-3x$

Step 1: Use distributive property.

$-8x+4>5-3x$

Step 2: Use subtraction property of equality. Subtract 4 from both sides.

$-8x+4-4>5-3x-4$

$-8x>1-3x$

Step 3: Use addition property of equality. Add 3x on both sides.

$-5x>1$

Step 4: Use division property of equality. Divide both sides by -5. If an equality divide or multiply by a negative number, then the sing of inequality changes.

$x<-0.2$

Therefore the first step is distributive property. The solution of the given inequality is x<-0.2.

Answer 2

"We have, –4 (2x – 1) > 5 – 3x

⇒-8x + 4 > 5 – 3x

⇒-8x + 3x > 5 – 4

⇒-5x > 1

⇒5x <- 1

⇒$x\quad <\quad -\frac { 1 }{ 5 }$

Hence,$-4(2x-1)\quad >\quad 5-3x\quad <-\frac { 1 }{ 5 } .$

Steps to be followed to avoid the direction of inequality

1. In both sides,addition or subtraction should be done.
2. The positive number is used for multiplication and division"