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Math  /  Algebra

Question1. Solve each equation. a) (2x−5)(3x+8)=0(2 x-5)(3 x+8)=0

Studdy Solution

STEP 1

1. We are given the equation (2x−5)(3x+8)=0(2x - 5)(3x + 8) = 0.
2. We need to solve for xx.

STEP 2

1. Apply the Zero Product Property.
2. Solve each resulting equation separately.
3. List all solutions.

STEP 3

Apply the Zero Product Property, which states that if a product of factors is zero, then at least one of the factors must be zero. Therefore, set each factor equal to zero:
2x−5=0 2x - 5 = 0 3x+8=0 3x + 8 = 0

STEP 4

Solve the first equation 2x−5=02x - 5 = 0:
Add 5 to both sides:
2x=5 2x = 5
Divide both sides by 2:
x=52 x = \frac{5}{2}

STEP 5

Solve the second equation 3x+8=03x + 8 = 0:
Subtract 8 from both sides:
3x=−8 3x = -8
Divide both sides by 3:
x=−83 x = -\frac{8}{3}

STEP 6

List all solutions. The solutions to the equation (2x−5)(3x+8)=0(2x - 5)(3x + 8) = 0 are:
x=52andx=−83 x = \frac{5}{2} \quad \text{and} \quad x = -\frac{8}{3}
The solutions are:
52,−83 \boxed{\frac{5}{2}, -\frac{8}{3}}

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