Answer :
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]
