After simplifying, get all the $x$ terms on one side of the inequality and the constant numbers on the other side, just like you would when solving a linear equation.

You will get something like $(\text{fraction})\cdot x \le \text{number}$. How do you undo the multiplication by a fraction, and what happens (or does not happen) to the inequality sign when you divide by a positive number?

Enter the left side as y1 = (5/3)x - 2 and the right side as y2 = (2/5)(x + 10) + 1 in Desmos so you see two straight lines on the graph.

Tap the point where the two lines intersect; Desmos will show the coordinates. The x-coordinate of this intersection is the boundary value where the two expressions are equal.

Make a table in Desmos for both functions (using the table icon) and look at an easy test value, such as $x = 0$. Compare $y_1$ and $y_2$ at that x-value to see whether $y_1 \le y_2$ is true there. Then note whether $0$ lies to the left or right of the intersection’s x-value; that tells you if the solution is all $x$ less than or equal to the boundary or all $x$ greater than or equal to it.

Start with the inequality

Distribute $\frac{2}{5}$ over $(x + 10)$:

So the inequality becomes

which simplifies to

Subtract $\frac{2}{5}x$ from both sides and add $2$ to both sides:

• Subtract $\frac{2}{5}x$:

• Add $2$:

Now the inequality has only $x$ terms on the left and a constant on the right.

Compute $\frac{5}{3} - \frac{2}{5}$:

So the inequality is

Now you have a simple one-step inequality of the form $ax \le b$.

To isolate $x$, divide both sides by $\frac{19}{15}$ (which is positive, so the inequality direction does not change). Dividing by $\frac{19}{15}$ is the same as multiplying by its reciprocal $\frac{15}{19}$:

Thus all real numbers satisfying the inequality are

which corresponds to choice C.