Question

Decide which of the choices below are solutions of 4x^2+8x-12=2(-2x+2). Circle yes or no for each. ChoicesX=1 yes or noX=-2 yes or no X=4 yes or noX=-4 yes or no

Answer 1

Given the expression;

`4x^2+8x-12=2(-2x+2)`

We can find the solution by simplifying the expression and factorizing the simplified expression to get the solutions.

`\begin{gathered} 4x^2+8x-12=-4x+4 \\ 4x^2+8x+4x-12-4=0 \\ 4x^2+12x-16=0 \\ 4(x^2+3x-4)=0 \\ \therefore x^2+3x-4=0 \end{gathered}`

We then factorize the quadratic expression above;

`\begin{gathered} x^2+3x-4=0 \\ the\text{ factors are +4 and -1} \\ x^2+4x-x-4=0 \\ x(x+4)-1(x+4)=0 \\ (x-1)(x+4)=0 \\ \end{gathered}`

Therefore the solutions would give;

`x=1,x=-4`

ANSWER: X=1 gives yes, x=-4 gives yes, the rest gives no