Answer :
To solve the equation [tex]\((2x - 3)(x + 4) = 0\)[/tex], we need to find the roots of the equation by setting each factor equal to zero.
1. Set [tex]\(2x - 3 = 0\)[/tex]:
[tex]\[ 2x - 3 = 0 \][/tex]
Add 3 to both sides:
[tex]\[ 2x = 3 \][/tex]
Now, divide both sides by 2:
[tex]\[ x = \frac{3}{2} \][/tex]
2. Set [tex]\(x + 4 = 0\)[/tex]:
[tex]\[ x + 4 = 0 \][/tex]
Subtract 4 from both sides:
[tex]\[ x = -4 \][/tex]
Thus, the roots of the equation are [tex]\(x = \frac{3}{2}\)[/tex] and [tex]\(x = -4\)[/tex]. Let's denote [tex]\(a = \frac{3}{2}\)[/tex] and [tex]\(b = -4\)[/tex].
We are asked to find the value of [tex]\(-a - b\)[/tex].
Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression:
[tex]\[ -a - b = -\left(\frac{3}{2}\right) - (-4) \][/tex]
First, compute the negation of [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[ -\left(\frac{3}{2}\right) = -\frac{3}{2} \][/tex]
Next, simplify the negation of [tex]\(-4\)[/tex]:
[tex]\[ -(-4) = 4 \][/tex]
Now, combine these results:
[tex]\[ -a - b = -\frac{3}{2} + 4 \][/tex]
Convert 4 to a fraction with a common denominator:
[tex]\[ 4 = \frac{8}{2} \][/tex]
Add the fractions:
[tex]\[ -\frac{3}{2} + \frac{8}{2} = \frac{-3 + 8}{2} = \frac{5}{2} \][/tex]
Therefore, the value of [tex]\(-a - b\)[/tex] is:
[tex]\[ \boxed{\frac{5}{2}} \][/tex]
1. Set [tex]\(2x - 3 = 0\)[/tex]:
[tex]\[ 2x - 3 = 0 \][/tex]
Add 3 to both sides:
[tex]\[ 2x = 3 \][/tex]
Now, divide both sides by 2:
[tex]\[ x = \frac{3}{2} \][/tex]
2. Set [tex]\(x + 4 = 0\)[/tex]:
[tex]\[ x + 4 = 0 \][/tex]
Subtract 4 from both sides:
[tex]\[ x = -4 \][/tex]
Thus, the roots of the equation are [tex]\(x = \frac{3}{2}\)[/tex] and [tex]\(x = -4\)[/tex]. Let's denote [tex]\(a = \frac{3}{2}\)[/tex] and [tex]\(b = -4\)[/tex].
We are asked to find the value of [tex]\(-a - b\)[/tex].
Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the expression:
[tex]\[ -a - b = -\left(\frac{3}{2}\right) - (-4) \][/tex]
First, compute the negation of [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[ -\left(\frac{3}{2}\right) = -\frac{3}{2} \][/tex]
Next, simplify the negation of [tex]\(-4\)[/tex]:
[tex]\[ -(-4) = 4 \][/tex]
Now, combine these results:
[tex]\[ -a - b = -\frac{3}{2} + 4 \][/tex]
Convert 4 to a fraction with a common denominator:
[tex]\[ 4 = \frac{8}{2} \][/tex]
Add the fractions:
[tex]\[ -\frac{3}{2} + \frac{8}{2} = \frac{-3 + 8}{2} = \frac{5}{2} \][/tex]
Therefore, the value of [tex]\(-a - b\)[/tex] is:
[tex]\[ \boxed{\frac{5}{2}} \][/tex]
