Frances solves the inequality 5g≥ 35. She says that 7 is a solution to the inequality. Is Frances correct? Explain
1 answer:
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<h3>Complete Question:</h3>
Given:
(1) DC = 6x, and DA = 4x + 18, find the value of x. Then find AD, DC, and AC
(2) EB = 4y - 12, and ED = y + 17. Find y. Then find ED, DB and EB.
<h3>Answer:</h3>
x = 9, AD = 54, DC = 54, AC = 108
y = 23, ED = 40, DB = 40, EB = 80
<h3>Step-by-step explanation:</h3>The diagram for this question has been attached to this response.
(1) From the diagram, it can be observed that;
(a) DC and DA have equal lengths. i.e
=> DC = DA ---------------------(i)
(b) AC = DA + DC --------------------(ii)
<em>But;</em>
DC = 6x
DA = 4x + 18
<em>Substitute the values of DC and DA into equation (i) as follows;</em>
6x = 4x + 18 [<em>Solve for x</em>]
6x - 4x = 18
2x = 18
x = 9
Since x = 9, then
DC = 6x = 6(9) = 54
DA = 4x + 18 = 4(9) + 18 = 54
<u>Therefore</u>
DC = 54
AD = DA = 54
AC = 54 + 54 = 108 [using equation (ii)]
(2) Also, from the diagram, it can be observed that;
(a) ED and DB have equal lengths. i.e
=> ED = DB ---------------------(iii)
(b) EB = ED + DB --------------------(iv)
=>EB = ED + ED [since ED = DB]
=>EB = 2ED ------------------(v)
<em>But;</em>
EB = 4y - 12
ED = y + 17
<em>Substitute the values of EB and ED into equation (v) as follows;</em>
4y - 12 = 2(y + 17) [<em>Solve for y</em>]
4y - 12 = 2y + 34
4y - 2y = 34 + 12
2y = 46
y = 46 / 2
y = 23
Since y = 23, then
EB = 4y - 12 = 4(23) - 12 = 80
ED = y + 17 = 23 + 17 = 40
<u>Therefore</u>
EB = 80
ED = DB = 40