Digital SAT Math Practice Question #1185
Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.
Before you begin solving, consider what values of \( x \) would make any part of the original equation undefined. These values must be excluded from your potential solutions.
When simplifying rational expressions, be careful when canceling terms. Ensure that the term you are canceling is not equal to zero for your potential solutions.
⚡ **Hack the Test: Backsolving and Domain Check** 1. **Check the domain restriction first:** Notice the denominator \( x-1 \). This immediately tells you that \( x eq 1 \). Any value of \( x \) that makes the denominator zero is not a valid solution. 2. **Eliminate options based on domain:** Option A (\( x=1 \)) and any option including \( x=1 \) (like Option C) can be immediately eliminated because \( x=1 \) makes the original equation undefined. This leaves Options B, D, and E. 3. **Backsolve with the remaining specific value:** The only specific value left in the options is \( x=3 \) (from Option D). Substitute \( x=3 \) into the original equation to check if it holds true: \[ \frac{3^2+1}{3-1} = \frac{2(3)}{3-1} + 2 \] \[ \frac{9+1}{2} = \frac{6}{2} + 2 \] \[ \frac{10}{2} = 3 + 2 \] \[ 5 = 5 \] Since the equation holds true for \( x=3 \), Option D is the correct answer. This method is often quicker than full algebraic manipulation for multiple-choice questions with numerical options.
The problem asks for the value of \( x \) that satisfies the given equation, with the condition that \( x \) must be a real number. The equation is: \[ \frac{x^2+1}{x-1} = \frac{2x}{x-1} + 2 \] **Step 1: Identify restrictions on the variabl...
Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...
Unlock Full Solution & 2,600+ Official Drills
Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.
The function f(x) = -16x^2 + 64x + 80 models the height, in feet, of a ball x seconds after it is thrown into the air. W...
In the xy-plane, an angle with measure \( \theta \) radians is in standard position, and its terminal side passes throug...
Solve for $x$ where $2(3)^{x} = 54$....
If $f(x) = 4x - 1$ and $g(x) = x + 3$, for what $x$ is $f(x) = g(x)$?...