Solved on Mar 04, 2024

Find the integer solution to the equation $(x+4)(5x+6)=0$ .

STEP 1

Assumptions
1. The given equation is $(x+4)(5x+6)=0$ .
2. We need to find the two solutions for $x$ .
3. One solution is an integer, and the other is a fraction.

STEP 2

To find the solutions for $x$ , we need to use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.

STEP 3

Set each factor equal to zero and solve for $x$ .
$x+4=0 \quad \text{and} \quad 5x+6=0$

STEP 4

Solve the first equation for $x$ .
$x+4=0$
$x=-4$

STEP 5

Solve the second equation for $x$ .
$5x+6=0$
$5x=-6$
$x=-\frac{6}{5}$

STEP 6

Now we have the two solutions for $x$ .
The integer solution is $x=-4$ and the fractional solution is $x=-\frac{6}{5}$ .
The integer solution is $-4$ .

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Find the integer solution to the equation $(x+4)(5x+6)=0$ .

STEP 1

Assumptions
1. The given equation is $(x+4)(5x+6)=0$ .
2. We need to find the two solutions for $x$ .
3. One solution is an integer, and the other is a fraction.

STEP 2

To find the solutions for $x$ , we need to use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.

STEP 3

Set each factor equal to zero and solve for $x$ .
$x+4=0 \quad \text{and} \quad 5x+6=0$

STEP 4

Solve the first equation for $x$ .
$x+4=0$
$x=-4$

STEP 5

Solve the second equation for $x$ .
$5x+6=0$
$5x=-6$
$x=-\frac{6}{5}$

STEP 6

Now we have the two solutions for $x$ .
The integer solution is $x=-4$ and the fractional solution is $x=-\frac{6}{5}$ .
The integer solution is $-4$ .

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Find the integer solution to the equation (x+4)(5x+6)=0(x+4)(5x+6)=0(x+4)(5x+6)=0.

STEP 1

Assumptions1. The given equation is (x+4)(5x+6)=0(x+4)(5x+6)=0(x+4)(5x+6)=0.2. We need to find the two solutions for xxx.3. One solution is an integer, and the other is a fraction.

STEP 2

To find the solutions for xxx, we need to use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.

STEP 3

Set each factor equal to zero and solve for xxx.x+4=0and5x+6=0x+4=0 \quad \text{and} \quad 5x+6=0x+4=0and5x+6=0

STEP 4

Solve the first equation for xxx.x+4=0x+4=0x+4=0x=−4x=-4x=−4

STEP 5

Solve the second equation for xxx.5x+6=05x+6=05x+6=05x=−65x=-65x=−6x=−65x=-\frac{6}{5}x=−56​

STEP 6

Now we have the two solutions for xxx.The integer solution is x=−4x=-4x=−4 and the fractional solution is x=−65x=-\frac{6}{5}x=−56​.The integer solution is −4-4−4.

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Find the integer solution to the equation $(x+4)(5x+6)=0$ .

Assumptions
1. The given equation is $(x+4)(5x+6)=0$ .
2. We need to find the two solutions for $x$ .
3. One solution is an integer, and the other is a fraction.

To find the solutions for $x$ , we need to use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero.

Set each factor equal to zero and solve for $x$ .
$x+4=0 \quad \text{and} \quad 5x+6=0$

Solve the first equation for $x$ .
$x+4=0$
$x=-4$

Solve the second equation for $x$ .
$5x+6=0$
$5x=-6$
$x=-\frac{6}{5}$

Now we have the two solutions for $x$ .
The integer solution is $x=-4$ and the fractional solution is $x=-\frac{6}{5}$ .
The integer solution is $-4$ .