Question

The solution of the given inequation where x ϵ R :- 7(x+3) + 4 ≤ 3(3x+ 9) is
a) x ≤ -1
b) x ≥ -1
c) x ≤ 0​

Answer 1

Answer:

b) x ≥ -1

Step-by-step explanation:

= 7(x+3)+4 ≤ 3(3x+9)

= 7x+21+4 ≤ 9x+27

= 7x+25 ≤ 9x+27

= 7x-9x ≤ 27-25

= -2x ≤ 2

As dividing by negative number in inequation the sign will be reversed according to rules

= x ≥ -2/2

=x ≥ -1

Answer 2

Question :

Solve the in-equation

7(x+3)+4 ≤ 3(3x+ 9) , x ε R

Theory :

Solution of linear equations :

1. Same number may be added to (or subtracted from ) both sides of an inequation without changing the sign of inequality.
2. The sign of inequality is reversed when both sides of an inequation are multipled or divided by a negative number .

Solution :

We have ,

$\sf\:7(x+3)+4\leqslant\:3(3x+9)$

$\sf\:7x+21+4\leqslant9x+27$

$\sf\:7x+25\leqslant\:9x+27$

$\sf\:7x-9x\leqslant\:27-25$

$\sf\:-2x\:\leqslant\:2$

Now divide both sides by 2 , then

$\sf\:-x\:\leqslant\:1$

Now multiply both sides by -1 , then

$\sf\:x\:\geqslant-1$

Therefore, correct option b) x ≥ -1