Question

The inequalities (1)/(5)x+7<=11 and -(1)/(5)x-7>=-11 share the same solutions. Solve the inequalities.

Answer 1

To solve the inequalities (1)/(5)x+7<=11 and -(1)/(5)x-7>=-11, isolate x in each inequality. Combine the solutions to find the shared solution.

Step-by-step explanation:

To solve the inequalities (1)/(5)x+7<=11 and -(1)/(5)x-7>=-11, we can start by isolating x. Let's solve the first inequality:

(1)/(5)x+7<=11

Subtract 7 from both sides:

(1)/(5)x<=4

Multiply both sides by 5 to remove the fraction:

x<=20

Now let's solve the second inequality:

-(1)/(5)x-7>=-11

Add 7 to both sides:

-(1)/(5)x>=-4

Multiply both sides by -5 to remove the fraction and reverse the inequality:

x<=20

Therefore, the shared solution for the two inequalities is x<=20.