Solve 2 ilepath3x+1 + 3 ilepath4x+5 = 23 for x.

Here are the solutions to your questions.

1. a) Solve $2\sqrt{3x+1} + 3\sqrt{4x+5} = 23$.

Step 1: Test for an integer solution. Let's try $x=5$.

$$2\sqrt{3(5)+1} + 3\sqrt{4(5)+5} = 2\sqrt{15+1} + 3\sqrt{20+5}$$ $$= 2\sqrt{16} + 3\sqrt{25}$$ $$= 2(4) + 3(5)$$ $$= 8 + 15$$ $$= 23$$

Since substituting $x=5$ satisfies the equation, $x=5$ is a solution.
The function $f(x) = 2\sqrt{3x+1} + 3\sqrt{4x+5}$ is a strictly increasing