Question

10.
$-4(5x - 2) - 24 = x + 3(x - 12) + 2$
11.
$8x + 7(2x - 10) - 6x = -4(-7x - 10) - x$

Explanation:

Problem 10: Solve \(-4(5x - 2) - 24 = x + 3(x - 12) + 2\)

Step 1: Expand both sides

Left side: \(-4(5x - 2) - 24 = -20x + 8 - 24\)
Right side: \(x + 3(x - 12) + 2 = x + 3x - 36 + 2\)

Step 2: Simplify both sides

Left side: \(-20x + 8 - 24 = -20x - 16\)
Right side: \(x + 3x - 36 + 2 = 4x - 34\)

Step 3: Move all x terms to left and constants to right

\(-20x - 4x = -34 + 16\)

Step 4: Combine like terms

\(-24x = -18\)

Step 5: Solve for x

\(x = \frac{-18}{-24} = \frac{3}{4}\)

Step 1: Expand both sides

Left side: \(8x + 14x - 70 - 6x\)
Right side: \(28x + 40 - x\)

Step 2: Simplify both sides

Left side: \(8x + 14x - 6x - 70 = 16x - 70\)
Right side: \(28x - x + 40 = 27x + 40\)

Step 3: Move all x terms to left and constants to right

\(16x - 27x = 40 + 70\)

Step 4: Combine like terms

\(-11x = 110\)

Step 5: Solve for x

\(x = \frac{110}{-11} = -10\)

Answer:

\(x = \frac{3}{4}\) (matches the pink color option)

Problem 11: Solve \(8x + 7(2x - 10) - 6x = -4(-7x - 10) - x\)