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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]  24 May 2019, 00:49
Expert's post
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]  24 May 2019, 13:02
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Expert's post
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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Brent Hanneson – Creator of greenlighttestprep.com

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