Answered

Explore IDNLearn.com's extensive Q&A database and find the answers you need. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

Ex: 4.1

Check whether the value given in the brackets is a solution to the given equation or not:

a. [tex]n = 1[/tex]
[tex]\[
\begin{array}{l}
n + 5 = 19(n - 1) \\
\text{LHS: } n + 5 \\
\Rightarrow 1 + 5 \\
\Rightarrow 6 \\
\text{RHS: } 19(n - 1) \\
\Rightarrow 19(1 - 1) \\
\Rightarrow 19 \cdot 0 \\
\Rightarrow 0 \\
\end{array}
\][/tex]
Therefore, [tex]n = 1[/tex] is not a solution.

b. [tex]n = -2[/tex]
[tex]\[
\begin{array}{l}
7n + 5 = 19(n + 2) \\
\text{LHS: } 7n + 5 \\
\Rightarrow 7(-2) + 5 \\
\Rightarrow -14 + 5 \\
\Rightarrow -9 \\
\text{RHS: } 19(n + 2) \\
\Rightarrow 19(-2 + 2) \\
\Rightarrow 19 \cdot 0 \\
\Rightarrow 0 \\
\end{array}
\][/tex]
Therefore, [tex]n = -2[/tex] is not a solution.

Sagot :

GinnyAnsweridn
Certainly! Let's go through each part of the question to check if the given values satisfy the equations:

### Part (a)
Given an equation:
[tex]\[ n + 5 = 19(n - 1) \][/tex]

We need to check if [tex]\( n = 1 \)[/tex] is a solution to this equation.

1. Substitute [tex]\( n = 1 \)[/tex] into the left-hand side (LHS):
[tex]\[ 1 + 5 = 6 \][/tex]

2. Substitute [tex]\( n = 1 \)[/tex] into the right-hand side (RHS):
[tex]\[ 19(1 - 1) = 19 \times 0 = 0 \][/tex]

3. Compare LHS and RHS:
[tex]\[ \text{LHS} = 6 \][/tex]
[tex]\[ \text{RHS} = 0 \][/tex]

Since 6 is not equal to 0, [tex]\( n = 1 \)[/tex] is not a solution to the equation.

### Part (b)
Given another equation:
[tex]\[ 7n + 5 = 19(n + 2) \][/tex]

We need to check if [tex]\( n = -2 \)[/tex] is a solution to this equation.

1. Substitute [tex]\( n = -2 \)[/tex] into the left-hand side (LHS):
[tex]\[ 7(-2) + 5 = -14 + 5 = -9 \][/tex]

2. Substitute [tex]\( n = -2 \)[/tex] into the right-hand side (RHS):
[tex]\[ 19(-2 + 2) = 19 \times 0 = 0 \][/tex]

3. Compare LHS and RHS:
[tex]\[ \text{LHS} = -9 \][/tex]
[tex]\[ \text{RHS} = 0 \][/tex]

Since -9 is not equal to 0, [tex]\( n = -2 \)[/tex] is not a solution to the equation.

### Summary:
- For equation [tex]\( n + 5 = 19(n - 1) \)[/tex], [tex]\( n = 1 \)[/tex] is not a solution.
- For equation [tex]\( 7n + 5 = 19(n + 2) \)[/tex], [tex]\( n = -2 \)[/tex] is not a solution.
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.