What are the solutions of the equation 4x^2-7x=3x+24

1.x= -4
2.x= -3
3.x= -3/2
4.x=2/3
5.x=2
6.x=4

6) x₁ = 4 and 3) x₂ = -3/2

Step-by-step explanation:

First we rearrange the terms:

4x²-7x = 3x + 24

4x²-7x -3x -24 = 0

4x²-11x -24 = 0

This is a quadratic equation having the form ax² + bx + c = 0

We can solve it by applying the formula:

x₁ = (10+22)/8 = 32/8 = 4

x₂ = (10-22)/8 = -12/8 = -3/2

6) x₁ = 4 and 3) x₂ = -3/2

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.