Questions: c. Is the equation (3 x^2+5 x-2=4 x^2) linear or quadratic? Choose the correct answer below. quadratic linear d. Is the equation (6^2 x+5=0) linear or quadratic? Choose the correct answer below. quadratic linear

Solution Steps

a. To solve the linear equation \(4x - 2 = 5\), we need to isolate \(x\) by first adding 2 to both sides and then dividing by 4.

b. For the quadratic equation \(2x^2 - 3 = -6\), we first add 6 to both sides to set the equation to zero, then solve for \(x\) using the quadratic formula.

c. The equation \(3x^2 + 5x - 2 = 4x^2\) is quadratic because it can be rearranged to the standard quadratic form \(ax^2 + bx + c = 0\).

To solve the equation \(4x - 2 = 5\), we first add 2 to both sides to get \(4x = 7\). Then, we divide both sides by 4 to isolate \(x\), resulting in \(x = \frac{7}{4}\).

First, we add 6 to both sides to set the equation to zero: \(2x^2 - 3 + 6 = 0\), which simplifies to \(2x^2 + 3 = 0\). Solving for \(x\), we find the solutions to be complex numbers: \(x = \frac{\pm \sqrt{6}i}{2}\).

Rearrange the equation to the standard quadratic form: \(3x^2 + 5x - 2 - 4x^2 = 0\), which simplifies to \(-x^2 + 5x - 2 = 0\). Since the equation contains an \(x^2\) term, it is a quadratic equation.

Final Answer