which are solutions of the equation 4x² - 7x = 3x + 24? check all that apply.\n□ x = -4\n□ x = -3\n□ x =…

which are solutions of the equation 4x² - 7x = 3x + 24? check all that apply.\n□ x = -4\n□ x = -3\n□ x = -3/2\n□ x = 2/3\n□ x = 2\n□ x = 4

which are solutions of the equation 4x² - 7x = 3x + 24? check all that apply.\n□ x = -4\n□ x = -3\n□ x = -3/2\n□ x = 2/3\n□ x = 2\n□ x = 4

Answer

Explanation:

Step1: Rearrange the equation

First, move all terms to one - side to get a quadratic equation in standard form $ax^{2}+bx + c = 0$. $4x^{2}-7x-3x - 24=0$, which simplifies to $4x^{2}-10x - 24 = 0$. Divide through by 2 to get $2x^{2}-5x - 12 = 0$.

Step2: Factor the quadratic equation

We need to find two numbers that multiply to $2\times(-12)=-24$ and add up to - 5. The numbers are - 8 and 3. So, $2x^{2}-8x + 3x-12 = 0$. Group the terms: $2x(x - 4)+3(x - 4)=0$. Then, $(2x + 3)(x - 4)=0$.

Step3: Solve for x

Set each factor equal to zero: If $2x+3 = 0$, then $2x=-3$, and $x=-\frac{3}{2}$. If $x - 4=0$, then $x = 4$.

Answer:

$x=-\frac{3}{2}$, $x = 4$