Question

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

Answer 1

Hello,
 the first step should be to distribue:
-4(3-5x)= -12+20x

Teh resolution may be:

-4(3-5x)>=-6x+9
==>-12+20x>=-6x+9
==>20x+6x>=9+12
==>26x>21
==>x>=21/26

But an other way may be used:

-4(3-5x)>=-6x+9
==>3-5x<= -6x/(-4)+9/(-4)
==>-5x-3/2 x<=-9/4 -3

==>-13/2 x <=-21/4

==>x>= -21/4 *(-2/13)
==>x>=21/(2*13)
==>x>=21/26

Answer 2

For this case we have the following inequality:

$-4 (3 - 5x) \geq-6x + 9$

To solve the inequality, we have as a first step to apply the distributive property on the left side of the inequality.

We have then:

$(-4) * (3) + (-4) * (- 5x) \geq-6x + 9$

Rewriting we have:

$-12+ 20x \geq -6x + 9$

Then, the following steps will only be mentioned:

1) Group variable terms on the left side of the inequality

2) Group constant terms on the right side of the inequality

3) Add the variable terms

4) Add the constant terms

5) Clear the value of x.

Answer:

a correct first step in solving the inequality is:

Distributive property:

$-12+ 20x \geq -6x + 9$