The question asks which number line represents the solution to 2x - 5 > 1. To solve, first add 5 to both sides: 2x > 6. Then divide both sides by 2: x > 3. Since we're dividing by a positive number, the inequality symbol remains unchanged. The solution x > 3 requires an open circle at 3 (since 3 is not included) with an arrow pointing to the right (representing all numbers greater than 3). A common error is using a closed circle when the inequality is strict (> or <) rather than inclusive (≥ or ≤). Remember that strict inequalities always use open circles to show the boundary point is excluded.

Test the pairs in the inequality $y < 4x - 7$.

* **Check A:**

* $(3, 4): 4 < 4(3) - 7 \rightarrow 4 < 5$ (True)

* $(5, 12): 12 < 4(5) - 7 \rightarrow 12 < 13$ (True)

For each of the others you'll find that one pair does not fit the inequality:

* Choice B: $(3, 5) \rightarrow 5 < 5$ (False, not strictly less).

* Choice C: $(2, 2) \rightarrow 2 < 1$ (False).

* Choice D: $(4, 10) \rightarrow 10 < 9$ (False).

Therefore, the correct answer is (3,4) and (5,12)

SAT Strategy

Notice the inequality is strict ($<$), not ($\le$). Therefore, if the LHS equals the RHS, the point is NOT a solution. For $x=3$, $4(3)-7=5$. So $y$ must be less than 5. Choice B has $y=5$ (reject). Choice A has $y=4$ (keep).

1. Variable weight: 45 lbs per box $\rightarrow 45b$.

2. Fixed weight: Driver $\rightarrow 180$.

3. Total weight must be less than or equal to limit: $45b + 180 \le 2,500$.

1. Subtract $2x$ from both sides: $2x - 7 \ge 5$.

2. Add 7 to both sides: $2x \ge 12$.

3. Divide by 2: $x \ge 6$.

SAT Strategy

On inequality problems, often you can pick a number that satisfies the potential answer. If you test $x=0$, the inequality becomes $-7 \ge 5$, which is False. Therefore, the solution cannot include 0. This eliminates B, C, and D (since 0 is less than 6, greater than -1, etc). Only A excludes 0.

In order to simplify this inequality, we'll want to start by subtracting 12 from both sides to arrive at 

$\frac{1}{4}x >3$

If we then multiply both sides of the inequality by 4 to cancel the coefficient in front of $x$, we get to 

$x>12$

Thus, 12 is not a possible value of x given the simplified inequality. 

Note - we could also solve this question by plugging each option in for $x$, but this route is likely somewhat more time consuming, so stay flexible in your approach on a question-to-question basis!