Question - Solve the Linear Equation for the Unknown Variable

Given equation: \( \frac{1}{2} (70 + 2x -10)(20) = \frac{1}{3}600 \)

Multiply through by 2 to get rid of the fraction: \( (70 + 2x - 10)(20) = \frac{2}{3}600 \)

Simplify inside the parentheses: \( (60 + 2x)(20) = \frac{2}{3}600 \)

Multiply out the parentheses: \( 1200 + 40x = \frac{2}{3}600 \)

Divide both sides by 40: \( x + 30 = \frac{2}{3} \times 15 \)

Divide 600 by 3: \( x + 30 = \frac{2}{3} \times 15 = 2 \times 5 = 10 \)

Subtract 30 from both sides: \( x = 10 - 30 \)

Therefore: \( x = -20 \)