(b) $$ 5(4 v+7) \leq 17 v+26 $$ No solution $$ v \leq $$ $$ \square $$ $$ v \geq $$ All real numbers are solutions

Question

UpStudy AI · Accepted Answer

To solve the inequality:

$$ 5(4v + 7) \leq 17v + 26 $$

**Step 1: Expand the left side**

$$ 5 \times 4v + 5 \times 7 = 20v + 35 $$

So the inequality becomes:

$$ 20v + 35 \leq 17v + 26 $$

**Step 2: Move all terms involving $$ v $$ to one side and constants to the other**

Subtract $$ 17v $$ from both sides:

$$ 20v - 17v + 35 \leq 26 $$

$$ 3v + 35 \leq 26 $$

Subtract 35 from both sides:

$$ 3v \leq 26 - 35 $$

$$ 3v \leq -9 $$

**Step 3: Solve for $$ v $$**

Divide both sides by 3:

$$ v \leq \frac{-9}{3} $$

$$ v \leq -3 $$

**Conclusion:**

The solution to the inequality is:

$$ v \leq -3 $$

So, the correct completion is:

$$ v \leq -3 $$
$$ v \leq -3 $$

(b) \( 5(4 v+7) \leq 17 v+26 \) No solution \( v \leq \) \( \square \) \( v \geq \) All real numbers are solutions