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.
• subtract 2x from both sides of the inequality.
• add 1 to both sides of the inequality.

Explanation:

To solve the inequality \(-4(2x - 1) > 5 - 3x\), the first step typically involves simplifying the left - hand side by using the distributive property. The distributive property states that \(a(b + c)=ab+ac\). For \(-4(2x - 1)\), we distribute \(-4\) to both \(2x\) and \(- 1\). So, \(-4\times2x=-8x\) and \(-4\times(-1) = 4\). This gives us \(-8x + 4>5 - 3x\).

Let's analyze the other options:

• The second option has a mistake in the distribution. \(-4\times(-1)\) should be \(4\), not \(-1\).
• Subtracting \(2x\) from both sides is not a logical first step as the left - hand side is in a factored form and needs to be expanded first.
• Adding \(1\) to both sides is also not a logical first step as the left - hand side is factored and should be expanded first.

Answer:

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