[Toán ?] Solve each equation.
Ngày 20/5/2017 bạn Ryan Nguyễn gửi bài tập:
Bài 1: Solve
a) $\frac{2m}{5}$ - 3 = $\frac{m}{2}$ - 1 b) d + $\frac{d}{2}$ = $\frac{d}{2}$ - 3
c) $\frac{3 + 2x}{7}$ = x + 4 d) $\frac{3}{4}$ - 7w = $\frac{6}{5}$ - 2w.
Giải:
a) $\frac{2m}{5}$ - 3 = $\frac{m}{2}$ - 1
<=> 2.2m - 3.10 = 5.m - 10 (quy đồng khử mẫu)
<=> 4m - 30 = 5m - 10
<=> 5m - 4m = -30 + 10
<=> m = -20
b) d + $\frac{d}{2}$ = $\frac{d}{2}$ - 3
<=> 6d + 3d = 2d - 3.6
<=> 9d - 2d = -18
<=> 7d = -18 <=> d = -$\frac{18}{7}$
c) $\frac{3 + 2x}{7}$ = x + 4
<=> 3 + 2x = 7x + 28
<=> 7x - 2x = 3 - 28
<=> 5x = -25 <=> x = -5
d) $\frac{3}{4}$ - 7w = $\frac{6}{5}$ - 2w.
<=> 3.5 - 7w.20 = 6.4 - 2w.20
<=> 15 - 140w = 24 - 40w
<=> 140w - 40w = 15 - 24
<=> 100w = -9 <=> w = -$\frac{9}{100}$
Bài 2: Solve each equation.
a) $\frac{2x + 1}{9}$ = 4 + x b) 1 - 3y = $\frac{y - 2}{4}$
c) $\frac{h + 1}{4}$ = $\frac{2h + 1}{3}$ d) $\frac{5c + 2}{3}$ + $\frac{2 - c}{2}$ = 0
e) $\frac{2u - 1}{3}$ + $\frac{3u - 1}{5}$ = 2 f) $\frac{4 - 2t}{3}$ - $\frac{5 + 2t}{4}$ = 0
g) $\frac{1}{2}$(3w - 2) + $\frac{1}{3}$(1 + w) = 4 h) $\frac{1}{4}$(2 - y) - $\frac{1}{3}$(y - 2) = 1
i) $\frac{x - 2}{3}$ + $\frac{1 + x}{2}$ = x j) $\frac{3 - n}{5}$ - $\frac{n + 1}{2}$ = 2n
k) $\frac{2(z - 2)}{3}$ + $\frac{3(1 + z)}{2}$ = 0 l) $\frac{3(1 - n)}{4}$ - $\frac{2(n - 1)}{3}$ = 3
Giải:
a) $\frac{2x + 1}{9}$ = 4 + x
<=> 2x + 1 = 9(4 + x)
<=> 2x + 1 = 36 + 9x
<=> 9x - 2x = 1 - 36
<=> 7x = -35 <=> x = -5
b) 1 - 3y = $\frac{y - 2}{4}$
<=> 4(1 - 3y) = y - 2
<=> 4 - 12y = y - 2
<=> 12y + y = 4 + 2
<=> 13y = 6 <=> y = $\frac{6}{13}$
c) $\frac{h + 1}{4}$ = $\frac{2h + 1}{3}$
<=> 3(h + 1) = 4(2h + 1)
<=> 3h + 3 = 8h + 4
<=> 8h - 3h = 3 - 4
<=> 5h = -1 <=> h = -$\frac{1}{5}$
d) $\frac{5c + 2}{3}$ + $\frac{2 - c}{2}$ = 0
<=> 2(5c + 2) + 3(2 - c) = 0
<=> 10c + 4 + 6 - 3c = 0
<=> 7c = -10 <=> c = -$\frac{10}{7}$
e) $\frac{2u - 1}{3}$ + $\frac{3u - 1}{5}$ = 2
<=> 5(2u - 1) + 3(3u - 1) = 2.15
<=> 10u - 5 + 9u - 3 = 30
<=> 19u - 8 = 30
<=> 19u = 38 <=> u = 2
f) $\frac{4 - 2t}{3}$ - $\frac{5 + 2t}{4}$ = 0
<=> 4(4 - 2t) - 3(5 + 2t) = 0
<=> 16 - 8t - 15 - 2t = 0
<=> -10t + 1 = 0
<=> -10t = -1 <=> t = $\frac{1}{10}$
g) $\frac{1}{2}$(3w - 2) + $\frac{1}{3}$(1 + w) = 4
<=> 3(3w - 2) + 2(1 + w) = 4.6
<=> 9w - 6 + 2 + 2w = 24
<=> 11w = 24 + 6 - 2
<=> 11w = 28 <=> w = $\frac{28}{11}$
h) $\frac{1}{4}$(2 - y) - $\frac{1}{3}$(y - 2) = 1
<=> 3(2 - y) - 4(y - 2) = 12
<=> 6 - 3y - 4y + 8 = 12
<=> -7y = 12 - 14
<=> -7y = -2 <=> y = $\frac{2}{7}$
i) $\frac{x - 2}{3}$ + $\frac{1 + x}{2}$ = x
<=> 2(x - 2) + 3(1 + x) = 6x
<=> 2x - 4 + 3 + 3x = 6x
<=> 6x - 5x = -1
<=> x = -1
j) $\frac{3 - n}{5}$ - $\frac{n + 1}{2}$ = 2n
<=> 2(3 - n) - 5(n + 1) = 2n.10
<=> 6 - 2n - 5n - 5 = 20n
<=> 20n + 7n = 1
<=> 27n = 1 <=> n = $\frac{1}{27}$
k) $\frac{2(z - 2)}{3}$ + $\frac{3(1 + z)}{2}$ = 0
<=> 2.2(z - 2) + 3.3(1 + z) = 0
<=> 4z - 8 + 9 + 9z = 0
<=> 13z = -1 <=> z = -$\frac{1}{13}$
l) $\frac{3(1 - n)}{4}$ - $\frac{2(n - 1)}{3}$ = 3
<=> 3.3(1 - n) - 2.4(n - 1) = 3.12
<=> 9 - 9n - 8n + 8 = 36
<=> -17n = 36 - 17
<=> -17n = 19 <=> n = -$\frac{19}{17}$.
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Bài 1: Solve
a) $\frac{2m}{5}$ - 3 = $\frac{m}{2}$ - 1 b) d + $\frac{d}{2}$ = $\frac{d}{2}$ - 3
c) $\frac{3 + 2x}{7}$ = x + 4 d) $\frac{3}{4}$ - 7w = $\frac{6}{5}$ - 2w.
Giải:
a) $\frac{2m}{5}$ - 3 = $\frac{m}{2}$ - 1
<=> 2.2m - 3.10 = 5.m - 10 (quy đồng khử mẫu)
<=> 4m - 30 = 5m - 10
<=> 5m - 4m = -30 + 10
<=> m = -20
b) d + $\frac{d}{2}$ = $\frac{d}{2}$ - 3
<=> 6d + 3d = 2d - 3.6
<=> 9d - 2d = -18
<=> 7d = -18 <=> d = -$\frac{18}{7}$
c) $\frac{3 + 2x}{7}$ = x + 4
<=> 3 + 2x = 7x + 28
<=> 7x - 2x = 3 - 28
<=> 5x = -25 <=> x = -5
d) $\frac{3}{4}$ - 7w = $\frac{6}{5}$ - 2w.
<=> 3.5 - 7w.20 = 6.4 - 2w.20
<=> 15 - 140w = 24 - 40w
<=> 140w - 40w = 15 - 24
<=> 100w = -9 <=> w = -$\frac{9}{100}$
Bài 2: Solve each equation.
a) $\frac{2x + 1}{9}$ = 4 + x b) 1 - 3y = $\frac{y - 2}{4}$
c) $\frac{h + 1}{4}$ = $\frac{2h + 1}{3}$ d) $\frac{5c + 2}{3}$ + $\frac{2 - c}{2}$ = 0
e) $\frac{2u - 1}{3}$ + $\frac{3u - 1}{5}$ = 2 f) $\frac{4 - 2t}{3}$ - $\frac{5 + 2t}{4}$ = 0
g) $\frac{1}{2}$(3w - 2) + $\frac{1}{3}$(1 + w) = 4 h) $\frac{1}{4}$(2 - y) - $\frac{1}{3}$(y - 2) = 1
i) $\frac{x - 2}{3}$ + $\frac{1 + x}{2}$ = x j) $\frac{3 - n}{5}$ - $\frac{n + 1}{2}$ = 2n
k) $\frac{2(z - 2)}{3}$ + $\frac{3(1 + z)}{2}$ = 0 l) $\frac{3(1 - n)}{4}$ - $\frac{2(n - 1)}{3}$ = 3
Giải:
a) $\frac{2x + 1}{9}$ = 4 + x
<=> 2x + 1 = 9(4 + x)
<=> 2x + 1 = 36 + 9x
<=> 9x - 2x = 1 - 36
<=> 7x = -35 <=> x = -5
b) 1 - 3y = $\frac{y - 2}{4}$
<=> 4(1 - 3y) = y - 2
<=> 4 - 12y = y - 2
<=> 12y + y = 4 + 2
<=> 13y = 6 <=> y = $\frac{6}{13}$
c) $\frac{h + 1}{4}$ = $\frac{2h + 1}{3}$
<=> 3(h + 1) = 4(2h + 1)
<=> 3h + 3 = 8h + 4
<=> 8h - 3h = 3 - 4
<=> 5h = -1 <=> h = -$\frac{1}{5}$
d) $\frac{5c + 2}{3}$ + $\frac{2 - c}{2}$ = 0
<=> 2(5c + 2) + 3(2 - c) = 0
<=> 10c + 4 + 6 - 3c = 0
<=> 7c = -10 <=> c = -$\frac{10}{7}$
e) $\frac{2u - 1}{3}$ + $\frac{3u - 1}{5}$ = 2
<=> 5(2u - 1) + 3(3u - 1) = 2.15
<=> 10u - 5 + 9u - 3 = 30
<=> 19u - 8 = 30
<=> 19u = 38 <=> u = 2
f) $\frac{4 - 2t}{3}$ - $\frac{5 + 2t}{4}$ = 0
<=> 4(4 - 2t) - 3(5 + 2t) = 0
<=> 16 - 8t - 15 - 2t = 0
<=> -10t + 1 = 0
<=> -10t = -1 <=> t = $\frac{1}{10}$
g) $\frac{1}{2}$(3w - 2) + $\frac{1}{3}$(1 + w) = 4
<=> 3(3w - 2) + 2(1 + w) = 4.6
<=> 9w - 6 + 2 + 2w = 24
<=> 11w = 24 + 6 - 2
<=> 11w = 28 <=> w = $\frac{28}{11}$
h) $\frac{1}{4}$(2 - y) - $\frac{1}{3}$(y - 2) = 1
<=> 3(2 - y) - 4(y - 2) = 12
<=> 6 - 3y - 4y + 8 = 12
<=> -7y = 12 - 14
<=> -7y = -2 <=> y = $\frac{2}{7}$
i) $\frac{x - 2}{3}$ + $\frac{1 + x}{2}$ = x
<=> 2(x - 2) + 3(1 + x) = 6x
<=> 2x - 4 + 3 + 3x = 6x
<=> 6x - 5x = -1
<=> x = -1
j) $\frac{3 - n}{5}$ - $\frac{n + 1}{2}$ = 2n
<=> 2(3 - n) - 5(n + 1) = 2n.10
<=> 6 - 2n - 5n - 5 = 20n
<=> 20n + 7n = 1
<=> 27n = 1 <=> n = $\frac{1}{27}$
k) $\frac{2(z - 2)}{3}$ + $\frac{3(1 + z)}{2}$ = 0
<=> 2.2(z - 2) + 3.3(1 + z) = 0
<=> 4z - 8 + 9 + 9z = 0
<=> 13z = -1 <=> z = -$\frac{1}{13}$
l) $\frac{3(1 - n)}{4}$ - $\frac{2(n - 1)}{3}$ = 3
<=> 3.3(1 - n) - 2.4(n - 1) = 3.12
<=> 9 - 9n - 8n + 8 = 36
<=> -17n = 36 - 17
<=> -17n = 19 <=> n = -$\frac{19}{17}$.
Mỗi bài toán có nhiều cách giải, đừng quên chia sẻ cách giải hoặc ý kiến đóng góp của bạn ở khung nhận xét bên dưới. Xin cảm ơn!
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