What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?

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?

 

Answer 1

–2(5 – 4x) < 6x – 4?
Step 1: –10 + 8x < 6x – 4            [use distributive property]
Step 2: –10 < –2x – 4        [subtract +8x from both sides retains sense of inequality]
Step 3: –6 < –2x               [add +4 to both sides retains sense of inequality]
Step 4:  3 > x    [divide by -2 reverses sense of inequality; could be written x<3;]

 

Check value x=0:

  Is -2(5-4*0) < 6*0 - 4   ?

       -10 < -4   ?yes