Desmos Tricks

Absolute Value

Solve absolute value equations visually without splitting cases.

📏 Absolute Value Hack

Don't split into two cases. Just graph it.

y = |2x - 5| - 7

📝 SAT Problem

\[ |2x - 5| - 7 = 0 \]

What is the sum of the solutions to the given equation?

(A) 5
(B) 6
(C) 7
(D) 12

Step 1: Graph Digital SAT Absolute Value Desmos Hack

Type the equation into Desmos exactly as seen. You can set it equal to 0 or graph \(y = |2x - 5| - 7\).

|2x - 5| = 7

Step 2: Find x-intercepts to Solve Absolute Value Fast

Look for where the graph intersects the x-axis or the line \(y=7\).

Desmos Absolute Value Solution

The solutions are \(x = -1\) and \(x = 6\).

The sum is \(-1 + 6 = 5\).

💡 Alternative Approach: Graph y = |2x − 5| − 7

Instead of solving the equation algebraically, we can start by graphing:

y = |2x − 5| − 7

The solution to |2x − 5| − 7 = 0 is exactly where y = 0 — the x-intercepts of the graph.

Desmos graph of y = |2x - 5| - 7 showing x-intercepts at x = -1 and x = 6

From the graph, the V-shape crosses the x-axis at:

  • \(x = -1\)
  • \(x = 6\)

So the sum of the solutions is \(-1 + 6 = \mathbf{5}\).

✅ Final Answer:

5 (Answer choice A)

📐 Mastered Absolute Value?

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