Question

How to solve the following inequality -1 > -2(x - 4) -5(4x - 7)

Answer 1

Answer:

The solution of the inequality is:

$x>2$

Step-by-step explanation:

Given inequality:

$-1 >-2(x - 4)-5(4x-7)$

Solving the inequality.

Using distribution.

⇒ $-1 >(-2x) +((- 4)(-2))+(-5\times4x)+((-5)(-7))$

⇒ $-1 >-2x +8-20x+35$

Combining like terms

⇒ $-1 >-2x-20x+35+8$

⇒ $-1 >-22x +43$

Adding $22x$ both sides.

⇒ $-1+22x >-22x +43+22x$

⇒ $-1 +22x> 43$

Adding 1 both sides.

⇒ $-1+1 +22x> 43+1$

⇒ $22x>44$

Dividing both sides by 22.

⇒ $\frac{22x}{22}>\frac{44}{22}$

⇒ $x>2$

Thus, the solution of the inequality is:

$x>2$