Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & -4x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+105} & = & \color{red}{-112x} +40 \\\Leftrightarrow & -420x \color{red}{+105} \color{blue}{-105} \color{blue}{+112x} & = & \color{red}{-112x} +40 \color{blue}{+112x} \color{blue}{-105} \\\Leftrightarrow & -420x+112x& = & 40-105 \\\Leftrightarrow & \color{red}{-308} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-308} & & \\\Leftrightarrow & x = \frac{65}{308} & & \\ & V = \left\{ \frac{65}{308} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{11})& = & -3x+\frac{7}{12} \\\Leftrightarrow & 16x-\frac{20}{11}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2112}{ \color{blue}{132} }x- \frac{240}{ \color{blue}{132} })& = & (\frac{-396}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2112x \color{red}{-240} & = & \color{red}{-396x} +77 \\\Leftrightarrow & 2112x \color{red}{-240} \color{blue}{+240} \color{blue}{+396x} & = & \color{red}{-396x} +77 \color{blue}{+396x} \color{blue}{+240} \\\Leftrightarrow & 2112x+396x& = & 77+240 \\\Leftrightarrow & \color{red}{2508} x& = & 317 \\\Leftrightarrow & x = \frac{317}{2508} & & \\ & V = \left\{ \frac{317}{2508} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{9}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+63} & = & \color{red}{-175x} +40 \\\Leftrightarrow & 420x \color{red}{+63} \color{blue}{-63} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{-63} \\\Leftrightarrow & 420x+175x& = & 40-63 \\\Leftrightarrow & \color{red}{595} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{595} & & \\ & V = \left\{ \frac{-23}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-24} & = & \color{red}{35x} +2 \\\Leftrightarrow & 150x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & 150x-35x& = & 2+24 \\\Leftrightarrow & \color{red}{115} x& = & 26 \\\Leftrightarrow & x = \frac{26}{115} & & \\ & V = \left\{ \frac{26}{115} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{3})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -4x+\frac{10}{3}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{+20} & = & \color{red}{-30x} +7 \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+30x} & = & \color{red}{-30x} +7 \color{blue}{+30x} \color{blue}{-20} \\\Leftrightarrow & -24x+30x& = & 7-20 \\\Leftrightarrow & \color{red}{6} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{6} & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{7})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-48} & = & \color{red}{189x} +28 \\\Leftrightarrow & -168x \color{red}{-48} \color{blue}{+48} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{+48} \\\Leftrightarrow & -168x-189x& = & 28+48 \\\Leftrightarrow & \color{red}{-357} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-357} & & \\\Leftrightarrow & x = \frac{-76}{357} & & \\ & V = \left\{ \frac{-76}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -9x+\frac{9}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+9} & = & \color{red}{49x} +10 \\\Leftrightarrow & -63x \color{red}{+9} \color{blue}{-9} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-9} \\\Leftrightarrow & -63x-49x& = & 10-9 \\\Leftrightarrow & \color{red}{-112} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-112} & & \\\Leftrightarrow & x = \frac{-1}{112} & & \\ & V = \left\{ \frac{-1}{112} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{75x} +20 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+72} \\\Leftrightarrow & 270x-75x& = & 20+72 \\\Leftrightarrow & \color{red}{195} x& = & 92 \\\Leftrightarrow & x = \frac{92}{195} & & \\ & V = \left\{ \frac{92}{195} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -10x-\frac{4}{3}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x- \frac{20}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-20} & = & \color{red}{105x} +12 \\\Leftrightarrow & -150x \color{red}{-20} \color{blue}{+20} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{+20} \\\Leftrightarrow & -150x-105x& = & 12+20 \\\Leftrightarrow & \color{red}{-255} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-255} & & \\\Leftrightarrow & x = \frac{-32}{255} & & \\ & V = \left\{ \frac{-32}{255} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{16}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{80}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-80} & = & \color{red}{105x} +18 \\\Leftrightarrow & -240x \color{red}{-80} \color{blue}{+80} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{+80} \\\Leftrightarrow & -240x-105x& = & 18+80 \\\Leftrightarrow & \color{red}{-345} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-345} & & \\\Leftrightarrow & x = \frac{-98}{345} & & \\ & V = \left\{ \frac{-98}{345} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{4})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 28x-\frac{35}{4}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x- \frac{315}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{-315} & = & \color{red}{-108x} +8 \\\Leftrightarrow & 1008x \color{red}{-315} \color{blue}{+315} \color{blue}{+108x} & = & \color{red}{-108x} +8 \color{blue}{+108x} \color{blue}{+315} \\\Leftrightarrow & 1008x+108x& = & 8+315 \\\Leftrightarrow & \color{red}{1116} x& = & 323 \\\Leftrightarrow & x = \frac{323}{1116} & & \\ & V = \left\{ \frac{323}{1116} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{+24} & = & \color{red}{110x} +55 \\\Leftrightarrow & 264x \color{red}{+24} \color{blue}{-24} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{-24} \\\Leftrightarrow & 264x-110x& = & 55-24 \\\Leftrightarrow & \color{red}{154} x& = & 31 \\\Leftrightarrow & x = \frac{31}{154} & & \\ & V = \left\{ \frac{31}{154} \right\} & \\\end{align}\)