Question

1. $4(2x - 5)-5x=-8$ 4) $12x - 7 = 9x+20$

Explanation:

Step1: Expand the left - hand side of equation 3

Expand $4(2x - 5)$ using the distributive property $a(b - c)=ab - ac$. So $4(2x - 5)=8x-20$. The equation $4(2x - 5)-5x=-8$ becomes $8x - 20-5x=-8$.
$8x - 20-5x=-8$

Step2: Combine like terms on the left - hand side of equation 3

Combine the $x$ terms: $8x-5x = 3x$. The equation is now $3x-20=-8$.
$3x-20=-8$

Step3: Isolate the variable term in equation 3

Add 20 to both sides of the equation: $3x-20 + 20=-8 + 20$. So $3x=12$.
$3x=12$

Step4: Solve for $x$ in equation 3

Divide both sides of the equation by 3: $\frac{3x}{3}=\frac{12}{3}$. So $x = 4$.
$x = 4$

Step5: Solve equation 4

Subtract $9x$ from both sides of the equation $12x-7=9x + 20$. We get $12x-9x-7=9x-9x + 20$, which simplifies to $3x-7=20$.
$3x-7=20$

Step6: Isolate the variable term in equation 4

Add 7 to both sides of the equation: $3x-7 + 7=20+7$. So $3x=27$.
$3x=27$

Step7: Solve for $x$ in equation 4

Divide both sides of the equation by 3: $\frac{3x}{3}=\frac{27}{3}$. So $x = 9$.
$x = 9$

Answer:

For equation $4(2x - 5)-5x=-8$, $x = 4$; for equation $12x-7=9x + 20$, $x = 9$