Bài 1: Giải phương trình.
1) 4x – 1 = 3x – 2.
2) 7 – 3x = 9 – x.
3) 15x – 10 = 10x + 15.
4) 4x – 7 = 3x + 6.
5) 6x – 1 = 7 + 2x.
6) 3(x – 1) = 2x – 1.
7) 3(x – 1) – 2(x + 3) = –15.
8) 2x – (3 – 5x) = 4(x + 3).
9) 5 – (x – 6) = 4(3 – 2x).
10) 3(x – 1) – (2x – 1) = 9 – x.
Đáp án:
Giải thích các bước giải:
`1) 4x – 1 = 3x – 2.`
`\to 4x-3x=-2+1`
`\to x=-1`
Vậy `x=-1`
,
`2) 7 – 3x = 9 – x.`
`\to -3+x=9-7`
`\to -2x=2`
`\to x=-1`
Vậy `x=-1`
,
`3) 15x – 10 = 10x + 15.`
`\to 15x-10x=15+10`
`\to 5x=25`
`\to x=25:5`
`\to x=5`
Vậy `x=5`
,
`4) 4x – 7 = 3x + 6`
`\to 4x-3x=6+7`
`\to x=13`
Vậy `x=13`
,
`5) 6x – 1 = 7 + 2x.`
`\to 6x-2x=7+1`
`\to 4x=8`
`\to x=8:4`
\to x=2`
Vậy `x=2`
,
`6) 3(x – 1) = 2x – 1`
`\to 3x-3=2x-1`
`\to 3x-2x=-1+3`
`\to x=2`
Vậy `x=2`
,
`7) 3(x – 1) – 2(x + 3) = –15.`
`\to 3x-3-2x-6=-15`
`\to x-9=-15`
`\to x=-15+9`
`\to x=-6`
Vậy `x=-6`
,
`8) 2x – (3 – 5x) = 4(x + 3).`
`\to 2x-3+5x=4x+12`
`\to 7x-4x=12+3`
`\to 3x=15`
`\to x=15:3`
`\to x=5`
Vậy `x=5`
,
`9) 5 – (x – 6) = 4(3 – 2x).`
`\to 5-x+6=12-8x`
`\to -x+8x=12-5-6`
`\to 7x=1`
`\to x=1/7`
Vậy `x=1/7`
,
`10) 3(x – 1) – (2x – 1) = 9 – x.`
`\to 3x-3-2x+1=9-x`
`\to x+x=9+2`
`\to 2x=11`
`\to x=11/2`
Vậy `x=11/2`
1) `4x-1=3x-2`
`<=> 4x-3x=-2+1`
`<=>x=-1`
Vậy `S={-1}`
2) `7-3x=9-x`
`<=> -3x+x=9-7`
`<=> -2x=2`
`<=>x=-1`
Vậy `S={-1}`
3) `15x-10=10x+15`
`<=> 15x-10x=15+10`
`<=> 5x=25`
`<=>x=5`
Vậy `S={5}`
4) `4x-7=3x+6`
`<=> 4x-3x=6+7`
`<=>x=13`
5) `6x-1=7+2x`
`<=>6x-2x=7+1`
`<=>4x=8`
`<=>x=2`
Vậy `S={2}`
6) `3(x-1)=2x-1`
`<=>3x-3=2x-1`
`<=>3x-2x=-1+3`
`<=>x=2`
Vậy `S={2}`
7) `3(x-1)-2(x+3)=-15`
`<=>3x-3-2x-6=-15`
`<=>x=-6`
Vậy `S={-6}`
8) `2x-(3-5x)=4(x+3)`
`<=> 2x-3+5x=4x+12`
`<=>7x-4x=12+3`
`<=>3x=15`
`<=>x=5`
Vậy `S={5}`
9) `5-(x-6)=4(3-2x)`
`<=>5-x+6=12-8x`
`<=>11-x=12-8x`
`<=>-x+8x=12-11`
`<=>7x=1`
`<=>x=1/7`
Vậy `S={1/7}`
10) `3(x-1)-(2x-1)=9-x`
`<=>3x-3-2x+1=9-x`
`<=>x-2=9-x`
`<=>x+x=9+2`
`<=>2x=11`
`<=>x=11/2`
Vậy `S={11/2}`