Solve the equation sqrt(4x-3) + sqrt(5x+1) = 2

May 20, 2026Mathematics

ScanSolve AI Answer

May 20, 2026

Step 1: Determine the domain of the variables. For the square roots to be defined, the expressions under them must be non-negative: $4x-3 \ge 0 \implies 4x \ge 3 \implies x \ge \frac{3}{4}$ $5x+1 \ge 0 \implies 5x \ge -1 \implies x \ge -\frac{1}{5}$ Combining these conditions, we must have $x \ge \frac{3}{4}$ . Since $x$ is specified as an integer, $x$ must be $1, 2, 3, \dots$ .

Step 2: Isolate one of the radical terms. Move the second radical term to the right side of the equation

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Determine the domain of the variables. For the square roots to be defined, the expressions under them must be non-negative: 4x-3 0 4x 3 x (3)/(4) 5x+1 0 5x -1 x -(1)/(5) Combining these conditions, we must have x (3)/(4).

Asked on May 20, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 20, 2026

Step 1: Determine the domain of the variables. For the square roots to be defined, the expressions under them must be non-negative: 4x-3 0 4x 3 x (3)/(4) 5x+1 0 5x -1 x -(1)/(5) Combining these conditions, we must have x (3)/(4). Since x is specified as an integer, x must be 1, 2, 3, . Step 2: Isolate one of the radical terms. Move the second radical term to the right side of the equation