Question Find values of $P$ that make the equation $3x - 5 = Px - 6$ have a unique solution.

Studdy Solution

STEP 1

Assumptions1. The given equation is $3x -5 = Px -6$ . We need to find the values of $$ that make this equation linear with only one solution

STEP 2

A linear equation in one variable has one solution if the coefficient of the variable is not equal to zero. In other words, the equation is linear if it can be written in the form $ax + b =0$ , where $a \neq0$ .

STEP 3

In the given equation, $3x -5 = Px -6$ , we can rearrange the terms to get it in the form $ax + b =0$ . $Px -3x =6 -5$

STEP 4

implify the equation.
$Px -3x =1$

STEP 5

Factor out $x$ on the left side of the equation.
$x(P -3) =1$

STEP 6

For the equation to be linear and have one solution, the coefficient of $x$ (which is $-3$ ) must not be equal to zero. Therefore, $-3 \neq0$ .

STEP 7

olve the inequality for $$.
$\neq3$ Therefore, the values of $$ that make the equation linear with only one solution are $-5$, $0$, $5$, and $-3$. The value $3$ is not included because it would make the coefficient of $x$ zero, resulting in an equation that is not linear.

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Question Find values of $P$ that make the equation $3x - 5 = Px - 6$ have a unique solution.

Studdy Solution

STEP 1

Assumptions1. The given equation is $3x -5 = Px -6$ . We need to find the values of $$ that make this equation linear with only one solution

STEP 2

A linear equation in one variable has one solution if the coefficient of the variable is not equal to zero. In other words, the equation is linear if it can be written in the form $ax + b =0$ , where $a \neq0$ .

STEP 3

In the given equation, $3x -5 = Px -6$ , we can rearrange the terms to get it in the form $ax + b =0$ . $Px -3x =6 -5$

STEP 4

implify the equation.
$Px -3x =1$

STEP 5

Factor out $x$ on the left side of the equation.
$x(P -3) =1$

STEP 6

For the equation to be linear and have one solution, the coefficient of $x$ (which is $-3$ ) must not be equal to zero. Therefore, $-3 \neq0$ .

STEP 7

olve the inequality for $$.
$\neq3$ Therefore, the values of $$ that make the equation linear with only one solution are $-5$, $0$, $5$, and $-3$. The value $3$ is not included because it would make the coefficient of $x$ zero, resulting in an equation that is not linear.

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Question Find values of PPP that make the equation 3x−5=Px−63x - 5 = Px - 63x−5=Px−6 have a unique solution.

Studdy Solution

STEP 1

Assumptions1. The given equation is 3x−5=Px−63x -5 = Px -63x−5=Px−6 . We need to find the values of $$ that make this equation linear with only one solution

STEP 2

A linear equation in one variable has one solution if the coefficient of the variable is not equal to zero. In other words, the equation is linear if it can be written in the form ax+b=0ax + b =0ax+b=0, where a≠0a \neq0a=0.

STEP 3

In the given equation, 3x−5=Px−63x -5 = Px -63x−5=Px−6, we can rearrange the terms to get it in the form ax+b=0ax + b =0ax+b=0.Px−3x=6−5Px -3x =6 -5Px−3x=6−5

STEP 4

implify the equation.Px−3x=1Px -3x =1Px−3x=1

STEP 5

Factor out xxx on the left side of the equation.x(P−3)=1x(P -3) =1x(P−3)=1

STEP 6

For the equation to be linear and have one solution, the coefficient of xxx (which is −3 -3−3) must not be equal to zero. Therefore, −3≠0 -3 \neq0−3=0.

STEP 7

olve the inequality for $$.≠3 \neq3=3Therefore, the values of $$ that make the equation linear with only one solution are $-5$, $0$, $5$, and $-3$. The value $3$ is not included because it would make the coefficient of $x$ zero, resulting in an equation that is not linear.

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Question Find values of $P$ that make the equation $3x - 5 = Px - 6$ have a unique solution.

Assumptions1. The given equation is $3x -5 = Px -6$ . We need to find the values of $$ that make this equation linear with only one solution

A linear equation in one variable has one solution if the coefficient of the variable is not equal to zero. In other words, the equation is linear if it can be written in the form $ax + b =0$ , where $a \neq0$ .

In the given equation, $3x -5 = Px -6$ , we can rearrange the terms to get it in the form $ax + b =0$ . $Px -3x =6 -5$

implify the equation.
$Px -3x =1$

Factor out $x$ on the left side of the equation.
$x(P -3) =1$

For the equation to be linear and have one solution, the coefficient of $x$ (which is $-3$ ) must not be equal to zero. Therefore, $-3 \neq0$ .

olve the inequality for $$.
$\neq3$ Therefore, the values of $$ that make the equation linear with only one solution are $-5$, $0$, $5$, and $-3$. The value $3$ is not included because it would make the coefficient of $x$ zero, resulting in an equation that is not linear.