Question

1. $2x - 10 + 0.5x = 2(x - 8) - 0.1$ 8. $12x + 12 - 3x = 3(2x + 4) - 15x$ $x = -2.44$ $x = -12.2$ $x = -24.4$ $varnothing$ $x = 0$ $infty$ red lime green black brown tan white

Explanation:

Problem 7: Solve \(2x - 10 + 0.5x = 2(x - 8) - 0.1\)

Step 1: Combine like terms on left

Combine \(2x\) and \(0.5x\): \(2x + 0.5x = 2.5x\), so left side is \(2.5x - 10\).

Step 2: Distribute on right

Distribute \(2\) in \(2(x - 8)\): \(2x - 16\), so right side is \(2x - 16 - 0.1 = 2x - 16.1\).

Step 3: Subtract \(2x\) from both sides

\(2.5x - 10 - 2x = 2x - 16.1 - 2x\) → \(0.5x - 10 = -16.1\).

Step 4: Add 10 to both sides

\(0.5x - 10 + 10 = -16.1 + 10\) → \(0.5x = -6.1\).

Step 5: Multiply by 2

\(x = -6.1 \times 2 = -12.2\).

Step 1: Combine like terms on left

\(12x - 3x = 9x\), so left side: \(9x + 12\).

Step 2: Distribute on right

\(3(2x + 4) = 6x + 12\), right side: \(6x + 12 - 15x = -9x + 12\).

Step 3: Add \(9x\) to both sides

\(9x + 12 + 9x = -9x + 12 + 9x\) → \(18x + 12 = 12\).

Step 4: Subtract 12

\(18x + 12 - 12 = 12 - 12\) → \(18x = 0\).

Step 5: Divide by 18

\(x = 0\).

Answer:

\(x = -12.2\) (lime green)

Problem 8: Solve \(12x + 12 - 3x = 3(2x + 4) - 15x\)