Question

X-5+15>8x-533x-5(x-7)<1​

Answer 1

X-5+15&gt=15-5=10=10-5+15=20
8x-53 3x-5(x-7)&lt=53-8

Answer 2

To solve this system of inequalities, let's start by simplifying each inequality individually and then solving for the variable x.

1. $x - 5 + 15 > 8x - 53$

First, combine like terms on both sides of the inequality:

$x + 10 > 8x - 53$

Next, isolate the variable x by moving all terms involving x to one side:

$x - 8x > -53 - 10$

$-7x > -63$

Now, divide both sides by -7. Remember to reverse the inequality sign because we're dividing by a negative number:

$\frac{-7x}{-7} < \frac{-63}{-7}$

$x < 9$

So, the solution to the first inequality is $x < 9$.

2. $3x - 5(x - 7) < 1$

First, distribute the -5 on the left side:

$3x - 5x + 35 < 1$

Combine like terms:

$-2x + 35 < 1$

Now, isolate the variable x:

$-2x < 1 - 35$

$-2x < -34$

To solve for x, divide both sides by -2. Remember to reverse the inequality sign again:

$\frac{-2x}{-2} > \frac{-34}{-2}$

$x > 17$

So, the solution to the second inequality is $x > 17$.

Now, you have two inequalities:

1. $x < 9$
2. $x > 17$

To find the solution for both inequalities combined, you need to find the intersection of these two solution sets. However, there is no overlap between $x < 9$ and $x > 17$. Therefore, there is no solution that satisfies both inequalities simultaneously. The solution set for this system of inequalities is an empty set, which means there is no value of x that satisfies both inequalities at the same time.