1001 Algebra Problems.PDF

170. d.
     a= ^7 b 4 –4
     4 a= 4^7 b 4 –4
     4 a= 7b– 4
     4 a+ 4 = 7b
     b= ^4 a 7 +4


171. b.
     ^2 x 5 +8= ^5 x 6 –6
     30 ^2 x 5 +8= 30^5 x 6 –6
     6(2x+ 8) = 5(5x– 6)
     12 x+ 48 = 25x–30
     12 x= 25x– 78
     –13x= –78
     x= 6


172. b.Let xbe the unknown number. The sentence
     “When ten is subtracted from the opposite of a
     number, the resulting difference is 5” can be
     expressed symbolically as the equation –x–10 =


173. We solve this equation for xas follows:

• x– 10 = 5


• x= 15
  x= –15

173. b.
     9 x+ ^83 = ^83 x+ 9
     3 (9x+ ^83 ) = 3(^83 x+ 9)
     27 x+ 8 = 8x+ 27
     27 x– 8x+ 8 = 27
     19 x= 27 – 8 = 19
     x= 1


174. c.Substitute F= 50 ̊ into the formula F= ^95 C

+ 32 and then solve the resulting equation for

C, as follows:

50 = ^95 C+ 32

5 50 = 5(^95 C+ 32)

250 = 9C+ 160

90 = C

C= 10

   175. d.Let xbe the unknown number. A 22.5%

      decrease in its value can be expressed symboli-

      cally as x– 0.225x= 0.775x. We are given that

      this quantity equals 93, which can be expressed

      as 0.775x = 93. We solve this equation for x:

0.775x= 93

x= 0.^973  75 = 120

176. c.The scenario described in this problem can
     be expressed as the equation 4(x+ 8) + 6x=
     2 x+ 32. We solve this equation for x:

4(x+ 8) + 6x= 2x+ 32

4 x+ 32 + 6x= 2x+ 32

10 x+ 32 = 2x+ 32

8 x= 0

x= 0

Set 12 (Page 21)

177. c.

=

15 = 15

5 (^12 x–4) = 3(x+ 8)

^52 x– 20 = 3x+ 24

2 (^52 x– 20) = 2(3x+ 24)

5 x– 40 = 6x+ 48

5 x– 88 = 6x

–88 = x

178. a.
     5 x– 2[x– 3(7 – x)] = 3 – 2(x– 8)
     5 x– 2x+ 6(7 – x) = 3 – 2(x– 8)
     5 x– 2x+ 42 – 6x) = 3 – 2x– 16
     –3x+ 42 = 19 – 2x
     23 = x

x+ 8

5

^12 x– 4

 3

x + 8

5

^12 x– 4

 3

ANSWERS & EXPLANATIONS–