Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

1. Tell which of the following is a linear equation in one variable:

a) [tex]x^2 - 4x + 3 = 0[/tex]

b) [tex]6x - 2y = 7[/tex]

c) [tex]3x - 1 = -2x[/tex]

d) [tex]pq - 3 = p[/tex]

e) [tex]3x + 2 = 4(x + 7) + 9[/tex]

Sagot :

GinnyAnswer
Let's analyze each given equation to determine if it is a linear equation in one variable:

a) [tex]\( x^2 - 4x + 3 = 0 \)[/tex]

This equation contains a term with [tex]\( x^2 \)[/tex], which means it is a quadratic equation. A linear equation in one variable should only have [tex]\( x \)[/tex] to the first power. Therefore, this is not a linear equation in one variable.

b) [tex]\( 6x - 2y = 7 \)[/tex]

This equation involves two variables, [tex]\( x \)[/tex] and [tex]\( y \)[/tex]. A linear equation in one variable should contain only one variable. Therefore, this is not a linear equation in one variable.

c) [tex]\( 3x - 1 = -2x \)[/tex]

To simplify this equation, we can combine like terms:
[tex]\[ 3x + 2x - 1 = 0 \][/tex]
[tex]\[ 5x - 1 = 0 \][/tex]

This simplifies to:
[tex]\[ 5x = 1 \][/tex]

This is a linear equation in one variable ([tex]\( x \)[/tex]). Therefore, it is a linear equation in one variable.

d) [tex]\( pq - 3 = p \)[/tex]

This equation involves two variables, [tex]\( p \)[/tex] and [tex]\( q \)[/tex], and it also contains a product term ([tex]\( pq \)[/tex]). A linear equation in one variable should involve only one variable and no products of variables. Therefore, this is not a linear equation in one variable.

e) [tex]\( 3x + 2 = 4(x + 7) + 9 \)[/tex]

To simplify this equation, first distribute the 4 on the right-hand side:
[tex]\[ 3x + 2 = 4x + 28 + 9 \][/tex]
[tex]\[ 3x + 2 = 4x + 37 \][/tex]

Next, move all the terms involving [tex]\( x \)[/tex] to one side and constants to the other side:
[tex]\[ 3x - 4x + 2 = 37 \][/tex]
[tex]\[ -x + 2 = 37 \][/tex]
[tex]\[ -x = 35 \][/tex]
[tex]\[ x = -35 \][/tex]

This simplifies to a linear equation in one variable ([tex]\( x \)[/tex]). Therefore, it is a linear equation in one variable.

In summary:
- Equation (a) is not a linear equation in one variable.
- Equation (b) is not a linear equation in one variable.
- Equation (c) is a linear equation in one variable.
- Equation (d) is not a linear equation in one variable.
- Equation (e) is a linear equation in one variable.

So, the linear equations in one variable among the given options are:
- [tex]\( c) \)[/tex] [tex]\( 3x - 1 = -2x \)[/tex]
- [tex]\( e) \)[/tex] [tex]\( 3x + 2 = 4(x + 7) + 9 \)[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.