Math Snap

STEP 1

1. We have two inequalities to solve: $1 - 4x \geq 25$ and $7x - 4 > 10$.
2. We need to find the solution set that satisfies both inequalities.
3. We will graph the solution set on a number line.

STEP 2

1. Solve the first inequality.
2. Solve the second inequality.
3. Find the intersection of the solution sets.
4. Graph the solution set.

STEP 3

Solve the first inequality: $1 - 4x \geq 25$.
Subtract 1 from both sides:
$$-4x \geq 24$$ Divide both sides by -4, remembering to reverse the inequality sign:
$$x \leq -6$$

STEP 4

Solve the second inequality: $7x - 4 > 10$.
Add 4 to both sides:
$$7x > 14$$ Divide both sides by 7:
$$x > 2$$

STEP 5

Find the intersection of the solution sets from the two inequalities.
The first inequality gives $x \leq -6$.
The second inequality gives $x > 2$.
Since there is no overlap between $x \leq -6$ and $x > 2$, the solution set is empty.

Graph the solution set.
Since the solution set is empty, there is nothing to graph on the number line.
The correct choice is:
E. The solution set is $\varnothing$.