Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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

(i) [tex]x + 5 = 3 \, \text{(}x = 2\text{)}[/tex]

(ii) [tex]8n + 5 = 21 \, \text{(}n = 2\text{)}[/tex]

(iii) [tex]4x + 3 = 5 \, \text{(}x = -2\text{)}[/tex]

(iv) [tex]5p + 3 = 7 \, \text{(}p = -3\text{)}[/tex]

(v) [tex]4p - 3 = 13 \, \text{(}p = 1\text{)}[/tex]

(vi) [tex]-3p - 2 = 10 \, \text{(}p = -4\text{)}[/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve each part one by one to check whether the given values are solutions to the respective equations.

### Part (i)
Equation: \( x + 5 = 3 \)
Given \( x = 2 \).

Substitute \( x = 2 \) into the equation:
[tex]\[ 2 + 5 = 7 \][/tex]
The right-hand side of the equation is 3, but the left-hand side, after substitution, gives 7.

Since \( 7 \neq 3 \), \( x = 2 \) is not a solution to \( x + 5 = 3 \).

### Part (ii)
Equation: \( 8n + 5 = 21 \)
Given \( n = 2 \).

Substitute \( n = 2 \) into the equation:
[tex]\[ 8(2) + 5 = 16 + 5 = 21 \][/tex]
Both sides of the equation are equal to 21.

Since \( 21 = 21 \), \( n = 2 \) is a solution to \( 8n + 5 = 21 \).

### Part (iii)
Equation: \( 4x + 3 = 5 \)
Given \( x = -2 \).

Substitute \( x = -2 \) into the equation:
[tex]\[ 4(-2) + 3 = -8 + 3 = -5 \][/tex]
The right-hand side of the equation is 5, but the left-hand side, after substitution, gives -5.

Since \( -5 \neq 5 \), \( x = -2 \) is not a solution to \( 4x + 3 = 5 \).

### Part (iv)
Equation: \( 5p + 3 = 7 \)
Given \( p = -3 \).

Substitute \( p = -3 \) into the equation:
[tex]\[ 5(-3) + 3 = -15 + 3 = -12 \][/tex]
The right-hand side of the equation is 7, but the left-hand side, after substitution, gives -12.

Since \( -12 \neq 7 \), \( p = -3 \) is not a solution to \( 5p + 3 = 7 \).

### Part (v)
Equation: \( 4p - 3 = 13 \)
Given \( p = 1 \).

Substitute \( p = 1 \) into the equation:
[tex]\[ 4(1) - 3 = 4 - 3 = 1 \][/tex]
The right-hand side of the equation is 13, but the left-hand side, after substitution, gives 1.

Since \( 1 \neq 13 \), \( p = 1 \) is not a solution to \( 4p - 3 = 13 \).

### Part (vi)
Equation: \( -3p - 2 = 10 \)
Given \( p = -4 \).

Substitute \( p = -4 \) into the equation:
[tex]\[ -3(-4) - 2 = 12 - 2 = 10 \][/tex]
Both sides of the equation are equal to 10.

Since \( 10 = 10 \), \( p = -4 \) is a solution to \( -3p - 2 = 10 \).

### Summary
To summarize, the given values are solutions to the equations as follows:
(i) \( x = 2 \): Not a solution
(ii) \( n = 2 \): Solution
(iii) \( x = -2 \): Not a solution
(iv) \( p = -3 \): Not a solution
(v) \( p = 1 \): Not a solution
(vi) [tex]\( p = -4 \)[/tex]: Solution
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.