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Solve each of the following equations for x. (a) 5x−7=28 (b)

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Solve each of the following equations for x. (a) 5x−7=28 (b) [#permalink] New post 24 May 2019, 00:49
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Solve each of the following equations for x.

(a) \(5x−7=28\)

(b) \(12−5x=x+30\)

(c) \(5(x+2)=1−3x\)

(d) \((x+6)(2x−1)=0\)

(e) \(x^2+5x−14=0\)

(f) \(x^2 −x−1=0\)

[Reveal] Spoiler: OA
(a) 7 (b) −3 (c) - \(\frac{9}{8}\) (d) \(-6,\frac{1}{2}\) (e) \(-7,2\) (f) \(\frac{1+\sqrt{5}}{2}, \frac{1-\sqrt{5}}{2}\)


Math Review
Question: 6
Page: 244
Difficulty: medium

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Re: Solve each of the following equations for x. (a) 5x−7=28 (b) [#permalink] New post 24 May 2019, 13:02
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Carcass wrote:
Solve each of the following equations for x.

(a) \(5x−7=28\)

(b) \(12−5x=x+30\)

(c) \(5(x+2)=1−3x\)

(d) \((x+6)(2x−1)=0\)

(e) \(x^2+5x−14=0\)

(f) \(x^2 −x−1=0\)

[Reveal] Spoiler: OA
(a) 7 (b) −3 (c) - \(\frac{9}{8}\) (d) \(-6,\frac{1}{2}\) (e) \(-7,2\) (f) \(\frac{1+\sqrt{5}}{2}, \frac{1-\sqrt{5}}{2}\)


Math Review
Question: 6
Page: 244
Difficulty: medium


(a) \(5x−7=28\)
Add 7 to both sides: \(5x=35\)
Divide both sides by 5 to get: \(x=7\)


(b) \(12−5x=x+30\)
Add 5x to both sides: \(12=6x+30\)
Subtract 30 from both sides: \(-18=6x\)
Divide both sides by 6 to get: \(-3=x\)

(c) \(5(x+2)=1−3x\)
Expand left side: \(5x+10=1−3x\)
Add 3x to both sides: \(8x+10=1\)
Subtract 10 from both sides: \(8x=-9\)
Divide both sides by 8 to get: \(x = -\frac{9}{8}\)


(d) \((x+6)(2x−1)=0\)
This means EITHER \(x+6=0\) OR \(2x-1=0\)
Solve \(x+6=0\) to get \(x=-6\)
Solve \(2x-1=0\) to get \(x = \frac{1}{2}\)


(e) \(x^2+5x−14=0\)
Factor: \((x+7)(x-2)=0\)
So, EITHER \(x=-7\) OR \(x=2\)

(f) \(x^2−x−1=0\)
Apply the quadratic formula to get:
\(x=\frac{1+\sqrt{5}}{2}\) or \(x=\frac{1-\sqrt{5}}{2}\)

Cheers,
Brent
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Re: Solve each of the following equations for x. (a) 5x−7=28 (b)   [#permalink] 24 May 2019, 13:02
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Solve each of the following equations for x. (a) 5x−7=28 (b)

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