Question 92·Medium·Linear Equations in One Variable

After distributing, combine the $x$ terms and the constant terms on each side to get a simpler equation, then move the $x$ terms to one side and the constants to the other.

Once you find $x$, remember the problem asks for $2x - 5$. Substitute your value of $x$ into that expression and simplify carefully, especially with fractions.

In one expression line, type y = 5(4 - x) + 3x. In another line, type y = 2(x + 7) + 1. These represent the left and right sides of the equation as two lines.

Use Desmos to locate the intersection point of the two lines. Click on the intersection; the x-coordinate of this point is the value of $x$ that satisfies the equation.

Take the x-value from the intersection (step 2) and, in a new expression line, type 2*(that x-value) - 5. Desmos will display a numerical result; choose the answer option that has the same value as this result.

Start with the equation:

Distribute on each side:

• Left side: $5(4 - x) = 20 - 5x$, so $5(4 - x) + 3x = 20 - 5x + 3x = 20 - 2x$.
• Right side: $2(x + 7) = 2x + 14$, so $2(x + 7) + 1 = 2x + 14 + 1 = 2x + 15$.

Now the equation is:

Solve $20 - 2x = 2x + 15$ by getting $x$ terms on one side and constants on the other:

Now you know the value of $x$; the question, however, asks for $2x - 5$, not $x$ itself.

Use $x = \dfrac{5}{4}$ in the expression $2x - 5$:

Write $5$ as $\dfrac{10}{2}$ so you can subtract:

So the value of $2x - 5$ is $-\dfrac{5}{2}$, which corresponds to choice D.