Once you have an equation like $-5x + 10 = 35$, use inverse operations (undo addition/subtraction, then multiplication/division) to isolate $x$.

After you know the value of $x$ that solves the original equation, plug that same $x$ into each answer choice. Which equation becomes a true statement?

Enter y = -5(x - 2) on one line and y = 35 on another line. Then find the point where the two graphs intersect; note the x-coordinate of this intersection, which is the solution of the original equation.

Using the x-value from the intersection, create a table or just type each left-hand side, like x - 2, and replace x with that value. Compare the result to the right-hand side of each option (for example, -7, 7, etc.) and see which equation becomes a true statement; that option has the same solution as the original equation.

Start with the given equation:

Distribute $-5$ across $(x - 2)$:

Now you have a simpler linear equation without parentheses.

From

subtract $10$ from both sides:

Now divide both sides by $-5$:

So the solution to the original equation is $x = -5$.

An equation has the same solution as the original if $x = -5$ makes it true.

Test each option by substituting $x = -5$:

• Option A: $x - 2 = -7$ becomes $-5 - 2 = -7$, which is true.
• Option B: $x - 2 = 7$ becomes $-5 - 2 = 7$, so $-7 = 7$, which is false.
• Option C: $x - 2 = -35$ becomes $-5 - 2 = -35$, so $-7 = -35$, which is false.
• Option D: $x - 2 = 175$ becomes $-5 - 2 = 175$, so $-7 = 175$, which is false.

Only option A) $x - 2 = -7$ is true when $x = -5$, so it is the equation with the same solution as the original.