- b.
^52 (x– 2) + 3x= 3(x + 2) – 10
^52 x– 5 + 3x= 3x+ 6 – 10
^121 x– 5 = 3x– 4
^121 x– 3x– 5 = –4
^52 x= –4 + 5 = 1
x= ^25
- c.Let xbe the unknown number. The sentence
“Twice a number increased by 11 is equal to 32
less than three times the number” can be
expressed symbolically as 2x+ 11 = 3x– 32.
We solve this equation for x, as follows:
2 x+ 11 = 3x– 32
2 x= 3x– 32 – 11
2 x– 3x= –43
- d.
^4 a 7 +4= –2– 4 ^3 a
28 ( ) = 28(–2– 4 ^3 a)
4(4a+ 4) = –7(2 – 3a)
16 a+ 16 = –14 + 21a
16 = –14 + 21a– 16a
16 + 14 = 5a
30 = 5a
a= 6
- a.Let xbe the smaller of the two unknown
integers. The next consecutive even integer is
then x+ 2. The sentence “The sum of two con-
secutive even integers is 126” can be expressed
symbolically as x+ (x+ 2) = 126. We solve this
equation for x:
x+ (x+ 2) = 126
2 x+ 2 = 126
2 x= 124
x= 62
Thus, the two integers are 62 and 64.
- b.
0.8(x+ 20) – 4.5 = 0.7(5 + x) – 0.9x
8(x+20) – 45 = 7(5 + x) – 9x
8 x+ 160 – 45 = 35 + 7x– 9x
8 x + 115 = 35 – 2x
10 x= –80
x= – 8
- e.First, we solve the equation 4x+ 5 = 15 for x:
4 x+ 5 = 15
4 x= 10
x= ^140 = 2.5
Now, substitute x = 2.5 into the expression
10 x + 5 to obtain 10(2.5) + 5 = 25 + 5 = 30.
- d.Let xbe the unknown number. 40% of this
number is represented symbolically as 0.40x.
Therefore, the sentence “Ten times 40% of a
number is equal to 4 less than six times the
number” can be expressed as the equation
10(0.40x) = 6x– 4. We solve this equation
for x:
10(0.40x) = 6x–4
4 x= 6x– 4
4 x+ 4 = 6x
4 = 2x
x= 2
- b.Let xbe the unknown number. The sentence
“^78 of nine times a number is equal to ten times
the number minus 17” can be expressed as the
equation ^78 (9x) = 10(x– 17). Solve this equa-
tion for x:
^78 (9x) = 10(x– 17)
8 ^78 (9x) = 810(x– 17)
63 x= 80(x– 17)
63 x= 80x– 1360
–17x= –1360
x= 80
^4 a+ 4
7
ANSWERS & EXPLANATIONS–
