If (2x - 3)(x + 4) = 0 and x > 0, what is the value of x? — SAT

If $(2x - 3)(x + 4) = 0$ and $x > 0$ , what is the value of $x$ ?

The value of

x

\frac{3}{2}

To find the solutions to the equation

(2x - 3)(x + 4) = 0

, we set each factor equal to zero. Setting

2x - 3 = 0

gives

x = \frac{3}{2}

, and setting

x + 4 = 0

gives

x = -4

. The problem states that

x > 0

, meaning the value of

x

must be positive. Therefore, the only valid solution is

\frac{3}{2}

Set each factor of the quadratic equation equal to zero using the zero product property.

2x - 3 = 0

x + 4 = 0

If the product of two factors is zero, then at least one of the individual factors must equal zero.

Solve each linear equation to find the possible values of

x

x = \frac{3}{2}

x = -4

Isolating

x

in each equation gives the roots of the quadratic equation.

Apply the given constraint

x > 0

to identify the correct solution.

x = \frac{3}{2}

is the only valid solution because

\frac{3}{2} > 0

and

-4 \ngtr 0

The problem restricts the solution to values of

x

that are strictly greater than zero, so the negative root must be discarded.

Solving factored quadratic equations with inequality constraints

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