Question

step 1: -10 + 8x < 6x - 4
step 2: -10 < -2x - 4
step 3: -6 < -2x
step 4: ______
what is the final step in solving the inequality -2(5 - 4x) < 6x - 4?
options:
x < -3
x < 3
x > 3
x > -3

Explanation:

Left Sub - question (Solving the inequality step - by - step)

Step 1: Given inequality

We start with the inequality \(-10 + 8x<6x - 4\).

Step 2: Subtract \(8x\) from both sides

Subtracting \(8x\) from both sides of the inequality \(-10 + 8x<6x - 4\) gives us \(-10<6x-8x - 4\), which simplifies to \(-10 < - 2x-4\).

Step 3: Add 4 to both sides

Adding 4 to both sides of the inequality \(-10 < - 2x-4\) gives us \(-10 + 4<-2x\), which simplifies to \(-6 < - 2x\).

Step 4: Divide by - 2 (and reverse inequality)

When we divide both sides of the inequality \(-6 < - 2x\) by \(-2\), we have to reverse the inequality sign. So, \(\frac{-6}{-2}>\frac{-2x}{-2}\), which simplifies to \(3 > x\) or \(x < 3\).

1. First, expand the left - hand side:

• Using the distributive property \(a(b - c)=ab - ac\), where \(a=-2\), \(b = 5\), and \(c = 4x\), we get \(-2\times5-(-2)\times4x<6x - 4\).
• Simplifying, we have \(-10 + 8x<6x - 4\).

1. Then, subtract \(8x\) from both sides:

• \(-10+8x - 8x<6x-8x - 4\), which simplifies to \(-10 < - 2x-4\).

1. Next, add 4 to both sides:

• \(-10 + 4<-2x-4 + 4\), which simplifies to \(-6 < - 2x\).

1. Finally, divide both sides by \(-2\) (and reverse the inequality sign):

• When we divide \(-6 < - 2x\) by \(-2\), we get \(\frac{-6}{-2}>\frac{-2x}{-2}\), so \(3 > x\) or \(x < 3\).

Answer:

\(x < 3\)

Right Sub - question (Solving the inequality \(-2(5 - 4x)<6x - 4\))