Questions: Solve 1. (x+3)(x+2)=0 2. (x+1)(x-2)=0 3. (x-1)(x-3)=0 4. 2x+1=0 5. 3x-1=0 6. (2x+1)(3x-1)=0 7. 1/2 x-1=0 8. 1/3 x+1=0 9. (1/2 x-1)(1/3 x+1)=0 10. (1/3 x-1/4)(1/2 x-3/7)=0

Transcript text: Solve 1. $(x+3)(x+2)=0$ 2. $(x+1)(x-2)=0$ 3. $(x-1)(x-3)=0$ 4. $2 x+1=0$ 5. $3 x-1=0$ 6. $(2 x+1)(3 x-1)=0$ 7. $\frac{1}{2} x-1=0$ 8. $\frac{1}{3} x+1=0$ 9. $\left(\frac{1}{2} x-1\right)\left(\frac{1}{3} x+1\right)=0$ 10. $\left(\frac{1}{3} x-\frac{1}{4}\right)\left(\frac{1}{2} x-\frac{3}{7}\right)=0$

Solution

Solution Steps

Solution Approach

For the equation $(x+3)(x+2)=0$, use the zero-product property which states that if a product of factors is zero, at least one of the factors must be zero. Solve for $x$ by setting each factor equal to zero: $x+3=0$ and $x+2=0$.
Similarly, for $(x+1)(x-2)=0$, apply the zero-product property. Set each factor equal to zero: $x+1=0$ and $x-2=0$.
For $(x-1)(x-3)=0$, use the zero-product property again. Set each factor equal to zero: $x-1=0$ and $x-3=0$.

Step 1: Solve $(x+3)(x+2)=0$

Using the zero-product property, we set each factor to zero: \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2 \] Thus, the solutions for this equation are $x = -3$ and $x = -2$.

Step 2: Solve $(x+1)(x-2)=0$

Again, applying the zero-product property: \[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \] \[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \] The solutions for this equation are $x = -1$ and $x = 2$.

Step 3: Solve $(x-1)(x-3)=0$

Using the zero-product property once more: \[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \] \[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \] The solutions for this equation are $x = 1$ and $x = 3$.