IDNLearn.com is the perfect place to get answers, share knowledge, and learn new things. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.
Sagot :
Sure! Let's go through each part step-by-step and solve the equations.
### Part (i)
The sum of 2 times [tex]\( x \)[/tex] and 5 is 18.
The equation can be written as:
[tex]\[ 2x + 5 = 18 \][/tex]
To solve for [tex]\( x \)[/tex], we first subtract 5 from both sides:
[tex]\[ 2x = 18 - 5 \][/tex]
[tex]\[ 2x = 13 \][/tex]
Next, we divide both sides by 2:
[tex]\[ x = \frac{13}{2} \][/tex]
So, the solution is:
[tex]\[ x = \frac{13}{2} \][/tex]
### Part (ii)
The sum of 5 times [tex]\( y \)[/tex] and 10 is 20.
The equation can be written as:
[tex]\[ 5y + 10 = 20 \][/tex]
To solve for [tex]\( y \)[/tex], we first subtract 10 from both sides:
[tex]\[ 5y = 20 - 10 \][/tex]
[tex]\[ 5y = 10 \][/tex]
Next, we divide both sides by 5:
[tex]\[ y = \frac{10}{5} \][/tex]
[tex]\[ y = 2 \][/tex]
So, the solution is:
[tex]\[ y = 2 \][/tex]
### Part (iii)
The sum of 4 times [tex]\( x \)[/tex] and 8 is 15.
The equation can be written as:
[tex]\[ 4x + 8 = 15 \][/tex]
To solve for [tex]\( x \)[/tex], we first subtract 8 from both sides:
[tex]\[ 4x = 15 - 8 \][/tex]
[tex]\[ 4x = 7 \][/tex]
Next, we divide both sides by 4:
[tex]\[ x = \frac{7}{4} \][/tex]
So, the solution is:
[tex]\[ x = \frac{7}{4} \][/tex]
### Part (iv)
Subtracting 6 from 3 times a number [tex]\( a \)[/tex] gives 12.
The equation can be written as:
[tex]\[ 3a - 6 = 12 \][/tex]
To solve for [tex]\( a \)[/tex], we add 6 to both sides:
[tex]\[ 3a = 12 + 6 \][/tex]
[tex]\[ 3a = 18 \][/tex]
Next, we divide both sides by 3:
[tex]\[ a = \frac{18}{3} \][/tex]
[tex]\[ a = 6 \][/tex]
So, the solution is:
[tex]\[ a = 6 \][/tex]
### Part (v)
Subtracting 2 times a number [tex]\( z \)[/tex] from 16 gives 3.
The equation can be written as:
[tex]\[ 16 - 2z = 3 \][/tex]
To solve for [tex]\( z \)[/tex], we first subtract 16 from both sides:
[tex]\[ -2z = 3 - 16 \][/tex]
[tex]\[ -2z = -13 \][/tex]
Next, we divide both sides by -2:
[tex]\[ z = \frac{-13}{-2} \][/tex]
[tex]\[ z = \frac{13}{2} \][/tex]
So, the solution is:
[tex]\[ z = \frac{13}{2} \][/tex]
### Part (vi)
Subtracting 5 from 4 times a number [tex]\( p \)[/tex] gives 7.
The equation can be written as:
[tex]\[ 4p - 5 = 7 \][/tex]
To solve for [tex]\( p \)[/tex], we add 5 to both sides:
[tex]\[ 4p = 7 + 5 \][/tex]
[tex]\[ 4p = 12 \][/tex]
Next, we divide both sides by 4:
[tex]\[ p = \frac{12}{4} \][/tex]
[tex]\[ p = 3 \][/tex]
So, the solution is:
[tex]\[ p = 3 \][/tex]
### Part (vii)
[tex]\( x \)[/tex] is 2 more than 5.
This can be written directly as:
[tex]\[ x = 5 + 2 \][/tex]
[tex]\[ x = 7 \][/tex]
So, the solution is:
[tex]\[ x = 7 \][/tex]
### Part (viii)
One-third of [tex]\( x \)[/tex] is 4 more than 8.
The equation can be written as:
[tex]\[ \frac{1}{3}x = 4 + 8 \][/tex]
Simplify the right-hand side:
[tex]\[ \frac{1}{3}x = 12 \][/tex]
To solve for [tex]\( x \)[/tex], multiply both sides by 3:
[tex]\[ x = 12 \times 3 \][/tex]
[tex]\[ x = 36 \][/tex]
So, the solution is:
[tex]\[ x = 36 \][/tex]
### Part (ix)
One-fourth of [tex]\( y \)[/tex] is 3 more than 9.
The equation can be written as:
[tex]\[ \frac{1}{4}y = 3 + 9 \][/tex]
Simplify the right-hand side:
[tex]\[ \frac{1}{4}y = 12 \][/tex]
To solve for [tex]\( y \)[/tex], multiply both sides by 4:
[tex]\[ y = 12 \times 4 \][/tex]
[tex]\[ y = 48 \][/tex]
So, the solution is:
[tex]\[ y = 48 \][/tex]
### Summary of Solutions
1. [tex]\( x = \frac{13}{2} \)[/tex]
2. [tex]\( y = 2 \)[/tex]
3. [tex]\( x = \frac{7}{4} \)[/tex]
4. [tex]\( a = 6 \)[/tex]
5. [tex]\( z = \frac{13}{2} \)[/tex]
6. [tex]\( p = 3 \)[/tex]
7. [tex]\( x = 7 \)[/tex]
8. [tex]\( x = 36 \)[/tex]
9. [tex]\( y = 48 \)[/tex]
### Part (i)
The sum of 2 times [tex]\( x \)[/tex] and 5 is 18.
The equation can be written as:
[tex]\[ 2x + 5 = 18 \][/tex]
To solve for [tex]\( x \)[/tex], we first subtract 5 from both sides:
[tex]\[ 2x = 18 - 5 \][/tex]
[tex]\[ 2x = 13 \][/tex]
Next, we divide both sides by 2:
[tex]\[ x = \frac{13}{2} \][/tex]
So, the solution is:
[tex]\[ x = \frac{13}{2} \][/tex]
### Part (ii)
The sum of 5 times [tex]\( y \)[/tex] and 10 is 20.
The equation can be written as:
[tex]\[ 5y + 10 = 20 \][/tex]
To solve for [tex]\( y \)[/tex], we first subtract 10 from both sides:
[tex]\[ 5y = 20 - 10 \][/tex]
[tex]\[ 5y = 10 \][/tex]
Next, we divide both sides by 5:
[tex]\[ y = \frac{10}{5} \][/tex]
[tex]\[ y = 2 \][/tex]
So, the solution is:
[tex]\[ y = 2 \][/tex]
### Part (iii)
The sum of 4 times [tex]\( x \)[/tex] and 8 is 15.
The equation can be written as:
[tex]\[ 4x + 8 = 15 \][/tex]
To solve for [tex]\( x \)[/tex], we first subtract 8 from both sides:
[tex]\[ 4x = 15 - 8 \][/tex]
[tex]\[ 4x = 7 \][/tex]
Next, we divide both sides by 4:
[tex]\[ x = \frac{7}{4} \][/tex]
So, the solution is:
[tex]\[ x = \frac{7}{4} \][/tex]
### Part (iv)
Subtracting 6 from 3 times a number [tex]\( a \)[/tex] gives 12.
The equation can be written as:
[tex]\[ 3a - 6 = 12 \][/tex]
To solve for [tex]\( a \)[/tex], we add 6 to both sides:
[tex]\[ 3a = 12 + 6 \][/tex]
[tex]\[ 3a = 18 \][/tex]
Next, we divide both sides by 3:
[tex]\[ a = \frac{18}{3} \][/tex]
[tex]\[ a = 6 \][/tex]
So, the solution is:
[tex]\[ a = 6 \][/tex]
### Part (v)
Subtracting 2 times a number [tex]\( z \)[/tex] from 16 gives 3.
The equation can be written as:
[tex]\[ 16 - 2z = 3 \][/tex]
To solve for [tex]\( z \)[/tex], we first subtract 16 from both sides:
[tex]\[ -2z = 3 - 16 \][/tex]
[tex]\[ -2z = -13 \][/tex]
Next, we divide both sides by -2:
[tex]\[ z = \frac{-13}{-2} \][/tex]
[tex]\[ z = \frac{13}{2} \][/tex]
So, the solution is:
[tex]\[ z = \frac{13}{2} \][/tex]
### Part (vi)
Subtracting 5 from 4 times a number [tex]\( p \)[/tex] gives 7.
The equation can be written as:
[tex]\[ 4p - 5 = 7 \][/tex]
To solve for [tex]\( p \)[/tex], we add 5 to both sides:
[tex]\[ 4p = 7 + 5 \][/tex]
[tex]\[ 4p = 12 \][/tex]
Next, we divide both sides by 4:
[tex]\[ p = \frac{12}{4} \][/tex]
[tex]\[ p = 3 \][/tex]
So, the solution is:
[tex]\[ p = 3 \][/tex]
### Part (vii)
[tex]\( x \)[/tex] is 2 more than 5.
This can be written directly as:
[tex]\[ x = 5 + 2 \][/tex]
[tex]\[ x = 7 \][/tex]
So, the solution is:
[tex]\[ x = 7 \][/tex]
### Part (viii)
One-third of [tex]\( x \)[/tex] is 4 more than 8.
The equation can be written as:
[tex]\[ \frac{1}{3}x = 4 + 8 \][/tex]
Simplify the right-hand side:
[tex]\[ \frac{1}{3}x = 12 \][/tex]
To solve for [tex]\( x \)[/tex], multiply both sides by 3:
[tex]\[ x = 12 \times 3 \][/tex]
[tex]\[ x = 36 \][/tex]
So, the solution is:
[tex]\[ x = 36 \][/tex]
### Part (ix)
One-fourth of [tex]\( y \)[/tex] is 3 more than 9.
The equation can be written as:
[tex]\[ \frac{1}{4}y = 3 + 9 \][/tex]
Simplify the right-hand side:
[tex]\[ \frac{1}{4}y = 12 \][/tex]
To solve for [tex]\( y \)[/tex], multiply both sides by 4:
[tex]\[ y = 12 \times 4 \][/tex]
[tex]\[ y = 48 \][/tex]
So, the solution is:
[tex]\[ y = 48 \][/tex]
### Summary of Solutions
1. [tex]\( x = \frac{13}{2} \)[/tex]
2. [tex]\( y = 2 \)[/tex]
3. [tex]\( x = \frac{7}{4} \)[/tex]
4. [tex]\( a = 6 \)[/tex]
5. [tex]\( z = \frac{13}{2} \)[/tex]
6. [tex]\( p = 3 \)[/tex]
7. [tex]\( x = 7 \)[/tex]
8. [tex]\( x = 36 \)[/tex]
9. [tex]\( y = 48 \)[/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.
