Download HOMEWORK 4 Question 4.1. x − 8=9 Solution. By adding 8 on both

HOMEWORK 4
RICKY NG
Question 4.1. x − 8 = 9
Solution. By adding 8 on both sides, we get x = 9 + 8 = 17.
Question 4.2. x + 2 = −8
Solution.
x + 2−2 = −8−2
x = −10
Question 4.3. 8x = 26
Solution. Divide by 8:
8x
26
=
8
8
13
13 × 2
=
x=
4×2
4
Question 4.4.
x
3
= 10
Solution. Multiply by 3:
x
×3 = 103
3
x = 30
Question 4.5. − 98 x = −4
Solution. Let’s do it step-by-step, first multiply by 9 to get grid of fraction:
8
− x×9 = −4×9
9
−8x = −36.
Now divide it by −8:
−8x
−36
=
−8
−8
−4 × 9
9
=
x=
−4 × 2
2
1
Question 4.6. 5x − 11 = 6
Solution. First get grid of −11 by adding:
5x − 11+11 = 6+11
5x = 17
5x
17
=
5
5
17
x=
5
Question 4.7. Solve for u, 32 u −
3
2
= 74 .
Solution. First find the common denominator, lcm(3, 2, 4) = 12. Multiply everything by
12, we get
3
7
2
12×( u − ) = ×12
3
2
4
2
3
12× u − 12× = 21
3
2
8u − 12 = 21.
To this end, we just treat it as a normal linear equation:
8u − 12+12 = 21+12
8u = 39
8u
39
=
8
8
39
u=
8
Question 4.8. 5x + 2 = −4x − 6
Solution. Group the x’s together, and get grid of numbers on LHS:
5x+4x + 2−2 = −4x+4x − 6−2
9x = −8
9x
−8
=
9
9
−8
x=
9
2
Question 4.9. −4(x + 3) − 5 = 2(x − 4) + 3
Solution. First get grid of parentheses by multiplying inside into each of the terms:
−4×x + −4×3 − 5 = 2×x − 2×4 + 3
−4x − 12 − 5 = 2x − 8 + 3
−4x − 17 = 2x − 5.
Now we separate x’s and constants:
−4x−2x − 17 + +17 = 2x−2x − 5+17
−6x = 12
−6x
12
=
−6
−6
x = −2
Question 4.10. Solve for c,
5
(c
49
− 7) = 17 c + 1
Solution. First get grid of fractions by finding out the common denominator, lcm(49, 7) =
49. Multiply everything by 49 we get
1
5
c+1
49× (c − 7) = 49×
49
7
5(c − 7) = 7c + 49.
Now unravel the parentheses by multiplying 5 into each term:
5c − 35 = 7c + 49.
Separate unknown and constants:
5c−7c − 35+35 = 7c−7c + 49+35
−2c = 84
−2c
84
=
−2
−2
c = −42
3