How do you use cross products to solve #2/t=5/(t-6)#?

Question

Isaiah Anthony · Accepted Answer

#t=-4#

Cross multiply the numerator by the denominator as in:

#2/t=5/(t-6)#

#2xx(t-6) = 5 xx t#

#2t-12 = 5t#

Add #12# both sides: #2t-12+12# = 5t+12#

#2t cancel(-12+12)# = 5t+12#

#2t = 5t+12# #2t-5t = 12# -----> making #t# the subject by subtracting #-5t# both sides:

#-3t=12#

#t=-12/3#

#t=-4#

Isaiah Anthony · Answer

#t=-4#

#"using the method of "color(blue)"cross-products"#

#•color(white)(x)a/b=c/drArrbc=ad#

#rArr5t=2(t-6)#

#rArr5t=2t-12#

#"subtract "2t" from both sides"#

#5t-2t=cancel(2t)cancel(-2t)-12#

#rArr3t=-12#

#"divide both sides by 3"#

#(cancel(3) t)/cancel(3)=(-12)/3#

#rArrt=-4#

#color(blue)"As a check"#

Substitute this value into the equation and if both sides are equal then it is the solution.

#"left "=2/(-4)=-1/2#

#"right "=5/(-4-6)=5/(-10)=-1/2#

#rArrt=-4" is the solution"#

Eva Adamson · Answer

undefined To solve the equation 2/t = 5/(t-6) using cross products, first cross multiply to get 2(t-6) = 5t. Expand and simplify the equation to get 2t - 12 = 5t. Rearrange terms to isolate t, resulting in -12 = 3t. Divide both sides by 3 to find t = -4.

Abigail Allen · Answer

undefined To solve $ \frac{2}{t} = \frac{5}{t-6} $ using cross multiplication:

$$ 2(t - 6) = 5t $$

$$ 2t - 12 = 5t $$

$$ 2t - 5t = 12 $$

$$ -3t = 12 $$

$$ t = -\frac{12}{3} $$

$$ t = -4 $$

Therefore, $ t = -4 $.