Solve the inequality: −34 < −2(4x − 1)

[tex]- 34 < - 2(4x - 1) \\ - 34 < - 8x + 2 \\ - 34 - 2 < - 8x \\ - 36 < - 8x \\ 36 8x \\ \frac{36}{8} x \\ x < \frac{9}{2}[/tex]

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that [tex]\frac{ab}{de}=\frac{bc}{ef}[/tex].

also, it is given that [tex]\frac{ab}{de}=\frac{3}{4}[/tex]

so, from the options, we need that [tex]\frac{bc}{ef}=\frac{3}{4}[/tex].

a. [tex]\frac{bc}{ef}=\frac{6}{9}=\frac{2}{3}[/tex]

b. [tex]\frac{bc}{ef}=\frac{4}{6}=\frac{2}{3}[/tex]

c.   [tex]\frac{bc}{ef}=\frac{8}{12}=\frac{2}{3}[/tex]

d. [tex]\frac{bc}{ef}=\frac{12}{16}=\frac{3}{4}[/tex]

as, we can see that only option d gives the same ratio as [tex]\frac{ab}{de}=\frac{3}{4}[/tex] i.e. [tex]\frac{bc}{ef}=\frac{3}{4}[/tex].

hence, the possible lengths are bc = 12 and ef = 16.

attachment?

step-by-step explanation: