Question

solve the following inequality for v. write your answer in simplest form. 6v - 5(8v - 8) < 7v - 7 - 10v

Explanation:

Step1: Expand left side

$6v - 40v + 40 < 7v -7 -10v$

Step2: Combine like terms both sides

$-34v + 40 < -3v -7$

Step3: Add 34v to both sides

$40 < 31v -7$

Step4: Add 7 to both sides

$47 < 31v$

Step5: Divide by 31

$\frac{47}{31} < v$ (rewrite as $v > \frac{47}{31}$ correction note: initial step 5 had typo; correct inequality direction after division by positive 31: $v > \frac{47}{31}$)

Wait correction: Let's redo precisely:

Step1: Expand left term

$6v - 40v + 40 < 7v -7 -10v$

Step2: Simplify both sides

$-34v + 40 < -3v -7$

Step3: Add 34v to both sides

$40 < 31v -7$

Step4: Add 7 to both sides

$47 < 31v$

Step5: Divide by 31 (positive, no flip)

$v > \frac{47}{31}$

Final correct answer: $v > \frac{47}{31}$ (or decimal approx 1.516, but exact form is better)

Answer:

$v < \frac{47}{31}$