23) x = [tex]\frac{-60}{9}[/tex] = -6.666.
24) x = [tex]\frac{-12}{7}[/tex] = -1.7142.
25) x = [tex]\frac{-37}{5}[/tex] = -7.4.
Step-by-step explanation:
Step 1; For [tex]\frac{x+6}{3}[/tex] = [tex]\frac{x+4}{12}[/tex], we cross multiply the denominators and get,
3 × (x + 4) = 12 × (x + 6),
3x + 12 = 12x + 72.
We take all the x terms to the LHS and keep the constants on the RHS.
3x - 12x = 72 - 12,
-9x = 60, x = [tex]\frac{-60}{9}[/tex] = -6.6666.
Step 2; For [tex]\frac{-5}{x-4}[/tex] = [tex]\frac{9}{x+12}[/tex], we cross multiply the denominators and get,
-5 × (x + 12) = 9 × (x - 4),
-5x - 60 = 9x - 36.
We take all the x terms to the LHS and keep the constants on the RHS.
-5x - 9x = -36 + 60,
-14x = 24, x = [tex]\frac{-24}{14}[/tex] = -1.7142.
Step 3; For [tex]\frac{6}{11}[/tex] = [tex]\frac{x-1}{x-8}[/tex], we cross multiply the denominators and get,
6 × (x - 8) = 11 × (x - 1),
6x - 48 = 11x - 11.
We take all the x terms to the LHS and keep the constants on the RHS.
6x - 11x = -11 + 48,
-5x = 37, x = [tex]\frac{-37}{5}[/tex] = -7.4.
