Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{3})& = & 3x+\frac{7}{11} \\\Leftrightarrow & 10x-\frac{10}{3}& = & 3x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-110} & = & \color{red}{99x} +21 \\\Leftrightarrow & 330x \color{red}{-110} \color{blue}{+110} \color{blue}{-99x} & = & \color{red}{99x} +21 \color{blue}{-99x} \color{blue}{+110} \\\Leftrightarrow & 330x-99x& = & 21+110 \\\Leftrightarrow & \color{red}{231} x& = & 131 \\\Leftrightarrow & x = \frac{131}{231} & & \\ & V = \left\{ \frac{131}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2520}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2520x \color{red}{+189} & = & \color{red}{-648x} +80 \\\Leftrightarrow & 2520x \color{red}{+189} \color{blue}{-189} \color{blue}{+648x} & = & \color{red}{-648x} +80 \color{blue}{+648x} \color{blue}{-189} \\\Leftrightarrow & 2520x+648x& = & 80-189 \\\Leftrightarrow & \color{red}{3168} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{3168} & & \\ & V = \left\{ \frac{-109}{3168} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 60x-50x& = & 45+24 \\\Leftrightarrow & \color{red}{10} x& = & 69 \\\Leftrightarrow & x = \frac{69}{10} & & \\ & V = \left\{ \frac{69}{10} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-18} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 315x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & 315x+147x& = & 14+18 \\\Leftrightarrow & \color{red}{462} x& = & 32 \\\Leftrightarrow & x = \frac{32}{462} & & \\\Leftrightarrow & x = \frac{16}{231} & & \\ & V = \left\{ \frac{16}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-360}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{-450}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -360x \color{red}{-80} & = & \color{red}{-450x} +27 \\\Leftrightarrow & -360x \color{red}{-80} \color{blue}{+80} \color{blue}{+450x} & = & \color{red}{-450x} +27 \color{blue}{+450x} \color{blue}{+80} \\\Leftrightarrow & -360x+450x& = & 27+80 \\\Leftrightarrow & \color{red}{90} x& = & 107 \\\Leftrightarrow & x = \frac{107}{90} & & \\ & V = \left\{ \frac{107}{90} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{11})& = & -2x+\frac{3}{4} \\\Leftrightarrow & 21x-\frac{14}{11}& = & -2x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{924}{ \color{blue}{44} }x- \frac{56}{ \color{blue}{44} })& = & (\frac{-88}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 924x \color{red}{-56} & = & \color{red}{-88x} +33 \\\Leftrightarrow & 924x \color{red}{-56} \color{blue}{+56} \color{blue}{+88x} & = & \color{red}{-88x} +33 \color{blue}{+88x} \color{blue}{+56} \\\Leftrightarrow & 924x+88x& = & 33+56 \\\Leftrightarrow & \color{red}{1012} x& = & 89 \\\Leftrightarrow & x = \frac{89}{1012} & & \\ & V = \left\{ \frac{89}{1012} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{11})& = & -4x+\frac{9}{7} \\\Leftrightarrow & 21x-\frac{21}{11}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1617}{ \color{blue}{77} }x- \frac{147}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1617x \color{red}{-147} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 1617x \color{red}{-147} \color{blue}{+147} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+147} \\\Leftrightarrow & 1617x+308x& = & 99+147 \\\Leftrightarrow & \color{red}{1925} x& = & 246 \\\Leftrightarrow & x = \frac{246}{1925} & & \\ & V = \left\{ \frac{246}{1925} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{11})& = & -3x+\frac{5}{8} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -3x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-704}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -704x \color{red}{+64} & = & \color{red}{-264x} +55 \\\Leftrightarrow & -704x \color{red}{+64} \color{blue}{-64} \color{blue}{+264x} & = & \color{red}{-264x} +55 \color{blue}{+264x} \color{blue}{-64} \\\Leftrightarrow & -704x+264x& = & 55-64 \\\Leftrightarrow & \color{red}{-440} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-440} & & \\\Leftrightarrow & x = \frac{9}{440} & & \\ & V = \left\{ \frac{9}{440} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{4})& = & -8x+\frac{3}{4} \\\Leftrightarrow & -21x+\frac{35}{4}& = & -8x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-84}{ \color{blue}{4} }x+ \frac{35}{ \color{blue}{4} })& = & (\frac{-32}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -84x \color{red}{+35} & = & \color{red}{-32x} +3 \\\Leftrightarrow & -84x \color{red}{+35} \color{blue}{-35} \color{blue}{+32x} & = & \color{red}{-32x} +3 \color{blue}{+32x} \color{blue}{-35} \\\Leftrightarrow & -84x+32x& = & 3-35 \\\Leftrightarrow & \color{red}{-52} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-52} & & \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{-40} & = & \color{red}{140x} +63 \\\Leftrightarrow & 224x \color{red}{-40} \color{blue}{+40} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{+40} \\\Leftrightarrow & 224x-140x& = & 63+40 \\\Leftrightarrow & \color{red}{84} x& = & 103 \\\Leftrightarrow & x = \frac{103}{84} & & \\ & V = \left\{ \frac{103}{84} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & -2x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-30} & = & \color{red}{-16x} +7 \\\Leftrightarrow & 120x \color{red}{-30} \color{blue}{+30} \color{blue}{+16x} & = & \color{red}{-16x} +7 \color{blue}{+16x} \color{blue}{+30} \\\Leftrightarrow & 120x+16x& = & 7+30 \\\Leftrightarrow & \color{red}{136} x& = & 37 \\\Leftrightarrow & x = \frac{37}{136} & & \\ & V = \left\{ \frac{37}{136} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{9})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 28x+\frac{35}{9}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x+ \frac{70}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{+70} & = & \color{red}{-162x} +63 \\\Leftrightarrow & 504x \color{red}{+70} \color{blue}{-70} \color{blue}{+162x} & = & \color{red}{-162x} +63 \color{blue}{+162x} \color{blue}{-70} \\\Leftrightarrow & 504x+162x& = & 63-70 \\\Leftrightarrow & \color{red}{666} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{666} & & \\ & V = \left\{ \frac{-7}{666} \right\} & \\\end{align}\)