Question

select the correct answer. which inequality represents all the solutions of 10(3x + 2) > 7(2x - 4)? a. x > -4 b. x < -4 c. x > -3 d. x < -3

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the inequality \(10(3x + 2)>7(2x - 4)\) using the distributive property \(a(b + c)=ab+ac\).
For the left - hand side: \(10(3x + 2)=10\times3x+10\times2 = 30x+20\)
For the right - hand side: \(7(2x - 4)=7\times2x-7\times4=14x - 28\)
So the inequality becomes \(30x + 20>14x-28\)

Step2: Move the terms with x to one side and constants to the other side

Subtract \(14x\) from both sides of the inequality: \(30x-14x + 20>14x-14x-28\)
Simplify: \(16x+20>-28\)
Then subtract 20 from both sides: \(16x+20 - 20>-28 - 20\)
Simplify: \(16x>-48\)

Step3: Solve for x

Divide both sides of the inequality \(16x>-48\) by 16. Since 16 is a positive number, the direction of the inequality sign remains the same.
\(\frac{16x}{16}>\frac{-48}{16}\)
Simplify: \(x>-3\)

Answer:

C. \(x > - 3\)