Bước 1: Giải câu a Ta có phương trình: 3x−4x+5x−13x=23 x minus 4 x plus 5 x minus one-third x equals 23𝑥−4𝑥+5𝑥−13𝑥=2.
Nhóm xx𝑥 làm nhân tử chung: x×(3−4+5−13)=2x cross open paren 3 minus 4 plus 5 minus one-third close paren equals 2𝑥×(3−4+5−13)=2.
Tính toán trong ngoặc: 3−4+5=43 minus 4 plus 5 equals 43−4+5=4. Sau đó lấy 4−13=12−13=1134 minus one-third equals the fraction with numerator 12 minus 1 and denominator 3 end-fraction equals eleven-thirds4−13=12−13=113.
Phương trình trở thành: 113x=2eleven-thirds x equals 2113𝑥=2.
x=2÷113=2×311=611x equals 2 divided by eleven-thirds equals 2 cross 3 over 11 end-fraction equals 6 over 11 end-fraction𝑥=2÷113=2×311=611
➡️ Bước 2: Giải câu b Phương trình: x+19+x+28+x+37=-3the fraction with numerator x plus 1 and denominator 9 end-fraction plus the fraction with numerator x plus 2 and denominator 8 end-fraction plus the fraction with numerator x plus 3 and denominator 7 end-fraction equals negative 3𝑥+19+𝑥+28+𝑥+37=−3.
Chuyển -3negative 3−3 sang vế trái và tách thành (-1)+(-1)+(-1)open paren negative 1 close paren plus open paren negative 1 close paren plus open paren negative 1 close paren(−1)+(−1)+(−1):
(x+19+1)+(x+28+1)+(x+37+1)=0open paren the fraction with numerator x plus 1 and denominator 9 end-fraction plus 1 close paren plus open paren the fraction with numerator x plus 2 and denominator 8 end-fraction plus 1 close paren plus open paren the fraction with numerator x plus 3 and denominator 7 end-fraction plus 1 close paren equals 0(𝑥+19+1)+(𝑥+28+1)+(𝑥+37+1)=0.
Quy đồng từng ngoặc:
x+1+99+x+2+88+x+3+77=0the fraction with numerator x plus 1 plus 9 and denominator 9 end-fraction plus the fraction with numerator x plus 2 plus 8 and denominator 8 end-fraction plus the fraction with numerator x plus 3 plus 7 and denominator 7 end-fraction equals 0𝑥+1+99+𝑥+2+88+𝑥+3+77=0
x+109+x+108+x+107=0the fraction with numerator x plus 10 and denominator 9 end-fraction plus the fraction with numerator x plus 10 and denominator 8 end-fraction plus the fraction with numerator x plus 10 and denominator 7 end-fraction equals 0𝑥+109+𝑥+108+𝑥+107=0
Đặt (x+10)open paren x plus 10 close paren(𝑥+10) làm nhân tử chung: (x+10)×(19+18+17)=0open paren x plus 10 close paren cross open paren one-nineth plus one-eighth plus one-seventh close paren equals 0(𝑥+10)×(19+18+17)=0.
Vì (19+18+17)≠0open paren one-nineth plus one-eighth plus one-seventh close paren is not equal to 0(19+18+17)≠0, nên ta có:
x+10=0⇒x=-10x plus 10 equals 0 implies x equals negative 10𝑥+10=0⇒𝑥=−10
➡️ Bước 3: Giải câu c Phương trình: 11.2x+12.3x+13.4x+…+19.10x=91 over 1.2 end-fraction x plus 1 over 2.3 end-fraction x plus 1 over 3.4 end-fraction x plus … plus 1 over 9.10 end-fraction x equals 911.2𝑥+12.3𝑥+13.4𝑥+…+19.10𝑥=9.
Đặt xx𝑥 làm nhân tử chung: x×(11.2+12.3+13.4+…+19.10)=9x cross open paren 1 over 1.2 end-fraction plus 1 over 2.3 end-fraction plus 1 over 3.4 end-fraction plus … plus 1 over 9.10 end-fraction close paren equals 9𝑥×(11.2+12.3+13.4+…+19.10)=9.
Sử dụng công thức tách phân số: 1n(n+1)=1n−1n+1the fraction with numerator 1 and denominator n open paren n plus 1 close paren end-fraction equals 1 over n end-fraction minus the fraction with numerator 1 and denominator n plus 1 end-fraction1𝑛(𝑛+1)=1𝑛−1𝑛+1.
Biểu thức trong ngoặc là: (1−12+12−13+13−…+19−110)open paren 1 minus one-half plus one-half minus one-third plus one-third minus … plus one-nineth minus one-tenth close paren(1−12+12−13+13−…+19−110).
Rút gọn ta được: 1−110=9101 minus one-tenth equals nine-tenths1−110=910.
Phương trình trở thành: x×910=9x cross nine-tenths equals 9𝑥×910=9.
x=9÷910=9×109=10x equals 9 divided by nine-tenths equals 9 cross ten-nineths equals 10𝑥=9÷910=9×109=10
✅ Đáp án: a) x=611x equals 6 over 11 end-fraction𝑥=𝟔𝟏𝟏
b) x=-10x equals negative 10𝑥=−𝟏𝟎
c) x=10x equals 10𝑥=𝟏𝟎