+0  
 
0
5
1
avatar+359 

Solve the inequality -4(x + 4) > x + 7 + 8x + 21.

 Apr 18, 2024
 #1
avatar+1616 
0

We can solve the inequality by distributing the terms, combining terms on each side, and isolating x. Here's how:

Distribute the terms on the left side: -4(x + 4) = -4x - 16

Combine terms on both sides: -4x - 16 > x + 7 + 8x + 21

Combine like terms: -4x - 16 > 9x + 28

Isolate x by getting all the x terms on one side: -13x - 16 > 28

Add 16 to both sides to isolate x further: -13x > 44

Divide both sides by -13 to isolate x (remembering to flip the inequality sign since we're dividing by a negative number): x < - \dfrac{44}{13}

Simplifying the answer: x < - \dfrac{33}{9}

Therefore, the solution to the inequality is the set of all real numbers less than - \dfrac{33}{9}. We can express this mathematically as: x ∈ {real numbers | x < - \dfrac{33}{9}}.

 Apr 18, 2024

0 Online Users