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(x+4)(2x-a)=0
In the given equation,
a is a constant. If the equation has the solutions
x=4 and
x=-4, what is the value of
a ?

$(x+4)(2 x-a)=0$ $\newline$ In the given equation, $a$ is a constant. If the equation has the solutions $x=4$ and $x=-4$ , what is the value of $a$ ?

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Write and solve direct variation equations

Full solution

Q.

(x+4)(2 x-a)=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=4

and

x=-4

, what is the value of

a

?

Identify Solutions: Identify the solutions of the equation. $\newline$ The given equation is in factored form, which means that the solutions for $x$ are the values that make each factor equal to zero. According to the problem, the solutions are $x=4$ and $x=-4$ .
Apply First Solution: Apply the first solution to the equation. $\newline$ If $x=4$ is a solution, then substituting $x=4$ into the equation $(x+4)(2x-a)=0$ should result in a true statement. Let's substitute $x=4$ into the equation and see what we get. $\newline$ $(4+4)(2\cdot 4-a)=0$ $\newline$ $(8)(8-a)=0$
Solve for $a$ : Solve for $a$ using the first solution. $\newline$ Since $(8)(8-a)=0$ , we know that one of the factors must be zero. The first factor, $8$ , is not zero, so the second factor, $8-a$ , must be zero. Therefore, we can set $8-a=0$ and solve for $a$ . $\newline$ $8-a=0$ $\newline$ $a=8$
Verify with Second Solution: Verify the solution with the second solution. $\newline$ Now we need to check if $a=8$ works for the second solution $x=-4$ . Substitute $x=-4$ into the equation $(x+4)(2x-a)=0$ with $a=8$ . $\newline$ $(-4+4)(2*(-4)-8)=0$ $\newline$ $(0)(-8-8)=0$ $\newline$ $(0)(-16)=0$
Confirm Correct Value: Confirm that the value of $a$ is correct. $\newline$ Since the second factor is zero when $x=-4$ , the equation is satisfied. This confirms that $a=8$ is the correct value for $a$ , as it works for both solutions $x=4$ and $x=-4$ .

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