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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.
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