Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(-5(5x-\frac{3}{4})=-9x+\frac{5}{4}\)
2. \(5(-4x+\frac{5}{8})=7x+\frac{9}{7}\)
3. \(-7(-2x-\frac{1}{2})=-5x+\frac{8}{11}\)
4. \(2(-4x+\frac{5}{9})=3x+\frac{9}{8}\)
5. \(-3(-4x-\frac{2}{7})=5x+\frac{8}{11}\)
6. \(-7(-2x-\frac{5}{4})=-3x+\frac{5}{12}\)
7. \(3(4x+\frac{2}{5})=-5x+\frac{8}{7}\)
8. \(-5(-4x+\frac{4}{7})=-9x+\frac{10}{3}\)
9. \(7(-2x-\frac{4}{3})=-3x+\frac{10}{3}\)
10. \(-3(-3x-\frac{5}{4})=5x+\frac{9}{7}\)
11. \(-7(3x-\frac{3}{11})=8x+\frac{6}{11}\)
12. \(-4(3x-\frac{2}{9})=-5x+\frac{2}{7}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{4})& = & -9x+\frac{5}{4} \\\Leftrightarrow & -25x+\frac{15}{4}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-100}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-36}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -100x \color{red}{+15} & = & \color{red}{-36x} +5 \\\Leftrightarrow & -100x \color{red}{+15} \color{blue}{-15} \color{blue}{+36x} & = & \color{red}{-36x} +5 \color{blue}{+36x} \color{blue}{-15} \\\Leftrightarrow & -100x+36x& = & 5-15 \\\Leftrightarrow & \color{red}{-64} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-64} & & \\\Leftrightarrow & x = \frac{5}{32} & & \\ & V = \left\{ \frac{5}{32} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{8})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -20x+\frac{25}{8}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x+ \frac{175}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{+175} & = & \color{red}{392x} +72 \\\Leftrightarrow & -1120x \color{red}{+175} \color{blue}{-175} \color{blue}{-392x} & = & \color{red}{392x} +72 \color{blue}{-392x} \color{blue}{-175} \\\Leftrightarrow & -1120x-392x& = & 72-175 \\\Leftrightarrow & \color{red}{-1512} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-1512} & & \\\Leftrightarrow & x = \frac{103}{1512} & & \\ & V = \left\{ \frac{103}{1512} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{1}{2})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 14x+\frac{7}{2}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{308}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 308x \color{red}{+77} & = & \color{red}{-110x} +16 \\\Leftrightarrow & 308x \color{red}{+77} \color{blue}{-77} \color{blue}{+110x} & = & \color{red}{-110x} +16 \color{blue}{+110x} \color{blue}{-77} \\\Leftrightarrow & 308x+110x& = & 16-77 \\\Leftrightarrow & \color{red}{418} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{418} & & \\ & V = \left\{ \frac{-61}{418} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{9})& = & 3x+\frac{9}{8} \\\Leftrightarrow & -8x+\frac{10}{9}& = & 3x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-576}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -576x \color{red}{+80} & = & \color{red}{216x} +81 \\\Leftrightarrow & -576x \color{red}{+80} \color{blue}{-80} \color{blue}{-216x} & = & \color{red}{216x} +81 \color{blue}{-216x} \color{blue}{-80} \\\Leftrightarrow & -576x-216x& = & 81-80 \\\Leftrightarrow & \color{red}{-792} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-792} & & \\\Leftrightarrow & x = \frac{-1}{792} & & \\ & V = \left\{ \frac{-1}{792} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+66} & = & \color{red}{385x} +56 \\\Leftrightarrow & 924x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +56 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & 924x-385x& = & 56-66 \\\Leftrightarrow & \color{red}{539} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{539} & & \\ & V = \left\{ \frac{-10}{539} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{4})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 14x+\frac{35}{4}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 4 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x+ \frac{105}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{+105} & = & \color{red}{-36x} +5 \\\Leftrightarrow & 168x \color{red}{+105} \color{blue}{-105} \color{blue}{+36x} & = & \color{red}{-36x} +5 \color{blue}{+36x} \color{blue}{-105} \\\Leftrightarrow & 168x+36x& = & 5-105 \\\Leftrightarrow & \color{red}{204} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{204} & & \\\Leftrightarrow & x = \frac{-25}{51} & & \\ & V = \left\{ \frac{-25}{51} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{6}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+42} & = & \color{red}{-175x} +40 \\\Leftrightarrow & 420x \color{red}{+42} \color{blue}{-42} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{-42} \\\Leftrightarrow & 420x+175x& = & 40-42 \\\Leftrightarrow & \color{red}{595} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{595} & & \\ & V = \left\{ \frac{-2}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-189x} +70 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{+60} \\\Leftrightarrow & 420x+189x& = & 70+60 \\\Leftrightarrow & \color{red}{609} x& = & 130 \\\Leftrightarrow & x = \frac{130}{609} & & \\ & V = \left\{ \frac{130}{609} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x-\frac{28}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{-28} & = & \color{red}{-9x} +10 \\\Leftrightarrow & -42x \color{red}{-28} \color{blue}{+28} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{+28} \\\Leftrightarrow & -42x+9x& = & 10+28 \\\Leftrightarrow & \color{red}{-33} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-33} & & \\\Leftrightarrow & x = \frac{-38}{33} & & \\ & V = \left\{ \frac{-38}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{4})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 9x+\frac{15}{4}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{+105} & = & \color{red}{140x} +36 \\\Leftrightarrow & 252x \color{red}{+105} \color{blue}{-105} \color{blue}{-140x} & = & \color{red}{140x} +36 \color{blue}{-140x} \color{blue}{-105} \\\Leftrightarrow & 252x-140x& = & 36-105 \\\Leftrightarrow & \color{red}{112} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{112} & & \\ & V = \left\{ \frac{-69}{112} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{11})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{21}{11}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+21} & = & \color{red}{88x} +6 \\\Leftrightarrow & -231x \color{red}{+21} \color{blue}{-21} \color{blue}{-88x} & = & \color{red}{88x} +6 \color{blue}{-88x} \color{blue}{-21} \\\Leftrightarrow & -231x-88x& = & 6-21 \\\Leftrightarrow & \color{red}{-319} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-319} & & \\\Leftrightarrow & x = \frac{15}{319} & & \\ & V = \left\{ \frac{15}{319} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{8}{9}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+56} & = & \color{red}{-315x} +18 \\\Leftrightarrow & -756x \color{red}{+56} \color{blue}{-56} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{-56} \\\Leftrightarrow & -756x+315x& = & 18-56 \\\Leftrightarrow & \color{red}{-441} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-441} & & \\\Leftrightarrow & x = \frac{38}{441} & & \\ & V = \left\{ \frac{38}{441} \right\} & \\\end{align}\)