Question 83·Medium·Linear Equations in One Variable

After distributing, combine the constant numbers on the left side so that your equation has one constant term and one $x$ term on each side.

Get all the $x$ terms on one side of the equation and all the constant terms on the other, then solve for $x$ using inverse operations (undoing addition/subtraction and then multiplication).

In one expression line, type y = 7 - 2(3x - 4) to graph the left-hand side of the equation.

In a new expression line, type y = 5x + 1 to graph the right-hand side.

Look for the point where the two lines intersect; click or tap that intersection and read the x-coordinate shown by Desmos. That x-value is the solution to the equation.

Start with the given equation: $7-2(3x-4)=5x+1$.

Distribute the $-2$ to both terms inside the parentheses:

• $-2\cdot 3x=-6x$
• $-2\cdot(-4)=+8$

So the left side becomes $7-6x+8$. Combine the constants $7$ and $8$ to get $15$, so the equation is now $15-6x=5x+1$.

Move all $x$ terms to one side and all constant terms to the other.

Add $6x$ to both sides to get rid of $-6x$ on the left:

Now subtract $1$ from both sides so that only the $x$ term remains on the right:

Solve $14=11x$ by dividing both sides by $11$.

This gives $x=\dfrac{14}{11}$, which corresponds to answer choice C.