Question

1. $-6(x - 4) = 2(x - 4)$
2. $2(4 - 5x) = 16 - 18x$
3. $-6(4 + 2x) = 2x - 52 - 10x$

Explanation:

Problem 19: $-6(x - 4) = 2(x - 4)$

Step 1: Expand both sides

Using the distributive property $a(b - c)=ab - ac$, we get:
$-6x + 24 = 2x - 8$

Step 2: Move all $x$ terms to one side

Add $6x$ to both sides:
$24 = 8x - 8$

Step 3: Solve for $x$

Add 8 to both sides:
$32 = 8x$
Divide both sides by 8:
$x = 4$

Step 1: Expand the left side

Using the distributive property $a(b - c)=ab - ac$, we get:
$8 - 10x = 16 - 18x$

Step 2: Move all $x$ terms to one side

Add $18x$ to both sides:
$8 + 8x = 16$

Step 3: Solve for $x$

Subtract 8 from both sides:
$8x = 8$
Divide both sides by 8:
$x = 1$

Step 1: Expand the left side and simplify the right side

Left side: Using the distributive property $a(b + c)=ab + ac$, we get $-24 - 12x$.
Right side: Combine like terms $2x - 10x=-8x$, so the right side is $-8x - 52$.
Now the equation is:
$-24 - 12x = -8x - 52$

Step 2: Move all $x$ terms to one side

Add $12x$ to both sides:
$-24 = 4x - 52$

Step 3: Solve for $x$

Add 52 to both sides:
$28 = 4x$
Divide both sides by 4:
$x = 7$

Answer:

$x = 4$

Problem 21: $2(4 - 5x) = 16 - 18x$