Question

c) $4h + 10 - 2h = 8$
show your check:
d) $\frac{z}{5} + 1 = -3$
show your check:
e) $3(2w - 4) = 6 + 2(w - 1)$
show your check:
f) $\frac{2b}{3} = \frac{40}{15}$
show your check:

Explanation:

Part (c)

Step1: Combine like terms

Simplify the left - hand side of the equation \(4h + 10-2h=8\). Combine the \(h\) terms: \(4h-2h = 2h\), so the equation becomes \(2h + 10=8\).

Step2: Subtract 10 from both sides

Subtract 10 from each side of the equation: \(2h+10 - 10=8 - 10\), which simplifies to \(2h=-2\).

Step3: Divide by 2

Divide both sides of the equation by 2: \(\frac{2h}{2}=\frac{-2}{2}\), so \(h = - 1\).

Step4: Check the solution

Substitute \(h=-1\) back into the original equation:
Left - hand side: \(4(-1)+10 - 2(-1)=-4 + 10+2=8\).
Right - hand side: \(8\).
Since the left - hand side equals the right - hand side, \(h=-1\) is correct.

Part (d)

Step1: Subtract 1 from both sides

For the equation \(\frac{z}{5}+1=-3\), subtract 1 from both sides: \(\frac{z}{5}+1 - 1=-3 - 1\), which gives \(\frac{z}{5}=-4\).

Step2: Multiply by 5

Multiply both sides of the equation by 5: \(5\times\frac{z}{5}=5\times(-4)\), so \(z=-20\).

Step3: Check the solution

Substitute \(z = - 20\) back into the original equation:
Left - hand side: \(\frac{-20}{5}+1=-4 + 1=-3\).
Right - hand side: \(-3\).
Since the left - hand side equals the right - hand side, \(z=-20\) is correct.

Part (e)

Step1: Distribute the coefficients

For the equation \(3(2w - 4)=6 + 2(w - 1)\), distribute on both sides.
Left - hand side: \(3\times2w-3\times4 = 6w-12\).
Right - hand side: \(6+2w-2=2w + 4\).
So the equation becomes \(6w-12=2w + 4\).

Step2: Subtract 2w from both sides

Subtract \(2w\) from both sides: \(6w-2w-12=2w-2w + 4\), which simplifies to \(4w-12 = 4\).

Step3: Add 12 to both sides

Add 12 to both sides: \(4w-12 + 12=4 + 12\), so \(4w=16\).

Step4: Divide by 4

Divide both sides by 4: \(\frac{4w}{4}=\frac{16}{4}\), so \(w = 4\).

Step5: Check the solution

Substitute \(w = 4\) back into the original equation:
Left - hand side: \(3(2\times4-4)=3(8 - 4)=3\times4 = 12\).
Right - hand side: \(6+2(4 - 1)=6+2\times3=6 + 6=12\).
Since the left - hand side equals the right - hand side, \(w = 4\) is correct.

Part (f)

Answer:

s:

• For part (c): \(h=-1\)
• For part (d): \(z = - 20\)
• For part (e): \(w = 4\)
• For part (f): \(b = 4\)