Rút gọn biểu thức $\color{blue}{P=1-\frac{1}{4}.(x:\frac{1}{10}-\frac{15}{4})-2.|3x-4|}$ khi:
$\color{blue}{a, x≥\frac{4}{3}}$
$\color{blue}{a, x<\frac{4}{3}}$
Rút gọn biểu thức $\color{blue}{P=1-\frac{1}{4}.(x:\frac{1}{10}-\frac{15}{4})-2.|3x-4|}$ khi:
$\color{blue}{a, x≥\frac{4}{3}}$
$\color{blue}{a, x<\frac{4}{3}}$
Đáp án:
Giải thích các bước giải:
P=1 -$\frac{1}{4}$ .(x : $\frac{1}{10}$ -$\frac{15}{4}$ ) -2.|3x -4|
=1 -$\frac{x}{40}$ +$\frac{15}{16}$ -2.|3x -4|
=$\frac{31}{16}$ -$\frac{x}{40}$ -2.|3x -4|
a) với x≥ $\frac{4}{3}$
P= $\frac{31}{16}$ -$\frac{x}{40}$ -2.(3x -4)
=$\frac{31}{16}$ -$\frac{x}{40}$ -6x +8
=-$\frac{241x}{40}$ +$\frac{159}{16}$
với x <$\frac{4}{3}$
P=$\frac{31}{16}$ -$\frac{x}{40}$ -2.(4 -3x)
=$\frac{31}{16}$ -$\frac{x}{40}$ -8 +6x
=$\frac{239x}{40}$ -$\frac{97}{16}$
Đáp án:
a, `x ≥ 4/3 => |3x – 4| = 3x – 4`
Ta có :
`P = 1 – 1/4 . (x : 1/10 – 15/4) – 2.|3x – 4|`
` = 1 – 1/4 . (10x – 15/4) – 2(3x – 4)`
` = 1 – 1/4 . ((40x – 15)/4) – (6x – 8)`
` = 1 – (40x – 15)/16 – 6x + 8`
` = 9 – ((40x – 15)/16 + (96x)/16)`
` = 9 – (40x – 15 + 96x)/16`
` = 9 – (136x – 15)/16`
` = 144/16 – (136x – 15)/16`
` = (144 – 136x – 15)/16`
` = (129 – 136x)/16`
b, `x < 4/3 => |3x – 4| = -(3x – 4) = 4 – 3x`
`=> P = 1 – 1/4 . (x : 1/10 – 15/4) – 2.|3x – 4|`
` = 1 – 1/4 . (10x – 15/4) – 2(4 – 3x)`
` = 1 – 1/4 . ((40x – 15)/4) – (8 – 6x)`
` = 1 – (40x – 15)/16 – 8 + 6x`
` = -7 + (96x)/16 – (40x – 15)/16`
` = -7 + (96x – 40x + 15)/16`
` = -7 + (56x + 15)/16`
` = -112/16 + (56x + 15)/16`
` = (-112 + 56x + 15)/16`
` = (56x – 97)/16`
Giải thích các bước giải: