Question 110·Medium·Linear Equations in One Variable

When you multiply by the common denominator, remember to multiply each term on both sides, including the $-3$ and the entire right-hand side.

After clearing fractions, distribute the numbers outside the parentheses, then combine constant terms so that you have a simpler equation with $x$ terms on both sides.

Once you have an equation like $ax + b = cx + d$, move all $x$ terms to one side and the constants to the other, then solve for $x$.

In Desmos, type the expression for the left-hand side as a function, for example: y1 = (2/5)(x-7) - 3.

On the next line, type the right-hand side as another function: y2 = (1/2)(x+3).

Look at the graph and tap or click the point where the two lines intersect. The x-coordinate of this intersection is the solution to the equation.

The denominators in the equation

are $5$ and $2$. The least common multiple of $5$ and $2$ is $10$, so multiply every term on both sides by $10$:

Now simplify each product:

• $10\cdot \frac{2}{5} = 4$
• $10\cdot 3 = 30$
• $10\cdot \frac12 = 5$

So the equation becomes

Distribute on both sides:

Combine the constants on the left:

Move all $x$ terms to one side and constants to the other. Subtract $4x$ from both sides:

Then subtract $15$ from both sides:

So $x = -73$, which matches choice C.) $-73$. This is the solution to the equation.