Question

Step 1: â€""10 8x < 6x â€"" 4 Step 2: â€""10 < â€""2x â€"" 4 Step 3: â€""6 < â€""2x Step 4: ________ What is the final step in solving the inequality â€""2(5 â€"" 4x) < 6x â€"" 4? x < â€""3 x > â€""3 x < 3 x > 3.

Answer 1

Option C:  x< 3 is the correct option as the fourth step of the simplification process of the given inequality.

Given inequality:

–2(5 – 4x) < 6x – 4

Step 1: –10 + 8x < 6x – 4

Step 2: –10 < –2x – 4

Step 3: –6 < –2x

Now the step 4 is division by -2 on both sides which flips the inequality:

Step 4: $\dfrac{-6}{-2} > \dfrac{-2x}{-2}\\\\= 3 > x\\= x < 3$

Thus option C: x < 3 is correct.

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