Question Find the number of solutions to the linear equation $8p + 1 = 4p + 2$ .

Studdy Solution

STEP 1

Assumptions1. The equation is linear in nature, i.e., the highest power of the variable (p) is1. . The equation is in the form $ap + b = cp + d$ , where a, b, c, and d are constants.

STEP 2

To find the number of solutions, we first need to simplify the equation. We start by bringing the terms involving 'p' to one side of the equation and the constant terms to the other side.
$8p -4p =2 -1$

STEP 3

implify the equation by performing the subtraction operations on both sides.
$p =1$

STEP 4

To isolate 'p', we divide both sides of the equation by4.
$p = \frac{1}{4}$

STEP 5

The equation is now in the form $p = constant$ , which means there is exactly one solution to the equation.
The solution to the equation is $p = \frac{1}{4}$ .

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Question Find the number of solutions to the linear equation $8p + 1 = 4p + 2$ .

Studdy Solution

STEP 1

Assumptions1. The equation is linear in nature, i.e., the highest power of the variable (p) is1. . The equation is in the form $ap + b = cp + d$ , where a, b, c, and d are constants.

STEP 2

To find the number of solutions, we first need to simplify the equation. We start by bringing the terms involving 'p' to one side of the equation and the constant terms to the other side.
$8p -4p =2 -1$

STEP 3

implify the equation by performing the subtraction operations on both sides.
$p =1$

STEP 4

To isolate 'p', we divide both sides of the equation by4.
$p = \frac{1}{4}$

STEP 5

The equation is now in the form $p = constant$ , which means there is exactly one solution to the equation.
The solution to the equation is $p = \frac{1}{4}$ .

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Question Find the number of solutions to the linear equation 8p+1=4p+28p + 1 = 4p + 28p+1=4p+2.

Studdy Solution

STEP 1

Assumptions1. The equation is linear in nature, i.e., the highest power of the variable (p) is1. . The equation is in the form ap+b=cp+dap + b = cp + dap+b=cp+d, where a, b, c, and d are constants.

STEP 2

To find the number of solutions, we first need to simplify the equation. We start by bringing the terms involving 'p' to one side of the equation and the constant terms to the other side.8p−4p=2−18p -4p =2 -18p−4p=2−1

STEP 3

implify the equation by performing the subtraction operations on both sides.p=1p =1p=1

STEP 4

To isolate 'p', we divide both sides of the equation by4.p=14p = \frac{1}{4}p=41​

STEP 5

The equation is now in the form p=constantp = constantp=constant, which means there is exactly one solution to the equation.The solution to the equation is p=14p = \frac{1}{4}p=41​.

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Question Find the number of solutions to the linear equation $8p + 1 = 4p + 2$ .

Assumptions1. The equation is linear in nature, i.e., the highest power of the variable (p) is1. . The equation is in the form $ap + b = cp + d$ , where a, b, c, and d are constants.

To find the number of solutions, we first need to simplify the equation. We start by bringing the terms involving 'p' to one side of the equation and the constant terms to the other side.
$8p -4p =2 -1$

implify the equation by performing the subtraction operations on both sides.
$p =1$

To isolate 'p', we divide both sides of the equation by4.
$p = \frac{1}{4}$

The equation is now in the form $p = constant$ , which means there is exactly one solution to the equation.
The solution to the equation is $p = \frac{1}{4}$ .