Question

which is a correct first step in solving the inequality $-4(2x - 1) > 5 - 3x$?

distribute $-4$ to get $-8x + 4 > 5 - 3x$.

distribute $-4$ to get $-8x - 1 > 5 - 3x$.

add 1 to both sides of the inequality.

subtract $2x$ from both sides of the inequality.

Explanation:

Step1: Recall the distributive property

The distributive property is \(a(b - c)=ab - ac\). For the left - hand side of the inequality \(-4(2x - 1)\), we apply the distributive property. Here, \(a=-4\), \(b = 2x\) and \(c = 1\). So, \(-4\times(2x)-(-4)\times1=-8x + 4\).

Step2: Analyze the other options

• For the option "Distribute \(-4\) to get \(-8x-1>5 - 3x\)": When we distribute \(-4\) over \((2x - 1)\), we should have \(-4\times2x-(-4)\times1=-8x + 4\), not \(-8x-1\). So this option is incorrect.
• For the option "Add 1 to both sides of the inequality": Adding 1 to both sides is not the first step. The first step should be to simplify the left - hand side by distributing \(-4\) over \((2x - 1)\) before performing operations like adding or subtracting terms to both sides.
• For the option "Subtract \(2x\) from both sides of the inequality": Subtracting \(2x\) from both sides is not the first step. We need to simplify the left - hand side using the distributive property first.

Answer:

Distribute \(-4\) to get \(-8x + 4>5 - 3x\).