9. $2(2x + 1)-3(x - 5)=18$ 10. $-(z+\frac{2}{3})=z$ 18. $3(x - 2)+2(x - 2)=40$ 19. $28=-7(2x - 3)$ 20. $-4(p…

Problem 9: (2(2x + 1)-3(x - 5)=18)

Explanation:

Step1: Expand the brackets

$$ \begin{align*} 2(2x + 1)-3(x - 5)&=18\ 4x+2-(3x - 15)&=18\ 4x + 2-3x+15&=18 \end{align*} $$

Step2: Combine like - terms

$$ \begin{align*} (4x-3x)+(2 + 15)&=18\ x+17&=18 \end{align*} $$

Step3: Solve for (x)

Subtract (17) from both sides: (x=18 - 17)

Answer:

(x = 1)

Problem 10: (-(z+\frac{2}{3})=z)

Explanation:

Step1: Expand the left - hand side

$$ \begin{align*} -(z+\frac{2}{3})&=z\ -z-\frac{2}{3}&=z \end{align*} $$

Step2: Move all terms with (z) to one side

Add (z) to both sides: (-\frac{2}{3}=z + z)

Step3: Combine like - terms and solve for (z)

$$ \begin{align*} 2z&=-\frac{2}{3}\ z&=-\frac{2}{3}\times\frac{1}{2} \end{align*} $$

Answer:

(z=-\frac{1}{3})

Problem 18: (3(x - 2)+2(x - 2)=40)

Explanation:

Step1: Factor out ((x - 2))

$$ \begin{align*} (3 + 2)(x - 2)&=40\ 5(x - 2)&=40 \end{align*} $$

Step2: Divide both sides by (5)

(x-2 = 8)

Step3: Solve for (x)

Add (2) to both sides: (x=8 + 2)

Answer:

(x = 10)

Problem 19: (28=-7(2x - 3))

Explanation:

Step1: Divide both sides by (-7)

$$ \begin{align*} \frac{28}{-7}&=2x-3\ -4&=2x-3 \end{align*} $$

Step2: Solve for (x)

Add (3) to both sides: (-4 + 3=2x), then (2x=-1), and (x=-\frac{1}{2})

Answer:

(x=-\frac{1}{2})

Problem 20: (-4(p + 2)+8=2(p - 1)-7p + 15)

Explanation:

Step1: Expand the brackets

$$ \begin{align*} -4p-8 + 8&=2p-2-7p + 15\ -4p&=-5p + 13 \end{align*} $$

Step2: Move all terms with (p) to one side

Add (5p) to both sides: (-4p+5p=13)

Answer:

(p = 13)

Problem 21: (2(5 - n)=6 + 6n)

Explanation:

Step1: Expand the left - hand side

$$ \begin{align*} 10-2n&=6 + 6n \end{align*} $$

Step2: Move all terms with (n) to one side

Add (2n) to both sides: (10=6 + 6n+2n), then (10=6 + 8n)

Step3: Solve for (n)

Subtract (6) from both sides: (4 = 8n), and (n=\frac{4}{8}=\frac{1}{2})

Answer:

(n=\frac{1}{2})