Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{3})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{20}{3}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+140} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 168x \color{red}{+140} \color{blue}{-140} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-140} \\\Leftrightarrow & 168x+63x& = & 6-140 \\\Leftrightarrow & \color{red}{231} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{231} & & \\ & V = \left\{ \frac{-134}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{7})& = & 8x+\frac{8}{11} \\\Leftrightarrow & -15x+\frac{15}{7}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+165} & = & \color{red}{616x} +56 \\\Leftrightarrow & -1155x \color{red}{+165} \color{blue}{-165} \color{blue}{-616x} & = & \color{red}{616x} +56 \color{blue}{-616x} \color{blue}{-165} \\\Leftrightarrow & -1155x-616x& = & 56-165 \\\Leftrightarrow & \color{red}{-1771} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1771} & & \\\Leftrightarrow & x = \frac{109}{1771} & & \\ & V = \left\{ \frac{109}{1771} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{+64} & = & \color{red}{-168x} +21 \\\Leftrightarrow & 240x \color{red}{+64} \color{blue}{-64} \color{blue}{+168x} & = & \color{red}{-168x} +21 \color{blue}{+168x} \color{blue}{-64} \\\Leftrightarrow & 240x+168x& = & 21-64 \\\Leftrightarrow & \color{red}{408} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{408} & & \\ & V = \left\{ \frac{-43}{408} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{9})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 16x+\frac{20}{9}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{+220} & = & \color{red}{495x} +81 \\\Leftrightarrow & 1584x \color{red}{+220} \color{blue}{-220} \color{blue}{-495x} & = & \color{red}{495x} +81 \color{blue}{-495x} \color{blue}{-220} \\\Leftrightarrow & 1584x-495x& = & 81-220 \\\Leftrightarrow & \color{red}{1089} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{1089} & & \\ & V = \left\{ \frac{-139}{1089} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & 8x+\frac{5}{11} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{+154} & = & \color{red}{264x} +15 \\\Leftrightarrow & 693x \color{red}{+154} \color{blue}{-154} \color{blue}{-264x} & = & \color{red}{264x} +15 \color{blue}{-264x} \color{blue}{-154} \\\Leftrightarrow & 693x-264x& = & 15-154 \\\Leftrightarrow & \color{red}{429} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{429} & & \\ & V = \left\{ \frac{-139}{429} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{175x} +15 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -315x-175x& = & 15+84 \\\Leftrightarrow & \color{red}{-490} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-490} & & \\\Leftrightarrow & x = \frac{-99}{490} & & \\ & V = \left\{ \frac{-99}{490} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{11})& = & -7x+\frac{5}{3} \\\Leftrightarrow & 6x-\frac{6}{11}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-18} & = & \color{red}{-231x} +55 \\\Leftrightarrow & 198x \color{red}{-18} \color{blue}{+18} \color{blue}{+231x} & = & \color{red}{-231x} +55 \color{blue}{+231x} \color{blue}{+18} \\\Leftrightarrow & 198x+231x& = & 55+18 \\\Leftrightarrow & \color{red}{429} x& = & 73 \\\Leftrightarrow & x = \frac{73}{429} & & \\ & V = \left\{ \frac{73}{429} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{9})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -14x-\frac{28}{9}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-28} & = & \color{red}{-27x} +24 \\\Leftrightarrow & -126x \color{red}{-28} \color{blue}{+28} \color{blue}{+27x} & = & \color{red}{-27x} +24 \color{blue}{+27x} \color{blue}{+28} \\\Leftrightarrow & -126x+27x& = & 24+28 \\\Leftrightarrow & \color{red}{-99} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-99} & & \\\Leftrightarrow & x = \frac{-52}{99} & & \\ & V = \left\{ \frac{-52}{99} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{9})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 28x+\frac{35}{9}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x+ \frac{70}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{+70} & = & \color{red}{-162x} +81 \\\Leftrightarrow & 504x \color{red}{+70} \color{blue}{-70} \color{blue}{+162x} & = & \color{red}{-162x} +81 \color{blue}{+162x} \color{blue}{-70} \\\Leftrightarrow & 504x+162x& = & 81-70 \\\Leftrightarrow & \color{red}{666} x& = & 11 \\\Leftrightarrow & x = \frac{11}{666} & & \\ & V = \left\{ \frac{11}{666} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{5})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 28x+\frac{14}{5}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1260}{ \color{blue}{45} }x+ \frac{126}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1260x \color{red}{+126} & = & \color{red}{405x} +10 \\\Leftrightarrow & 1260x \color{red}{+126} \color{blue}{-126} \color{blue}{-405x} & = & \color{red}{405x} +10 \color{blue}{-405x} \color{blue}{-126} \\\Leftrightarrow & 1260x-405x& = & 10-126 \\\Leftrightarrow & \color{red}{855} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{855} & & \\ & V = \left\{ \frac{-116}{855} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{490x} +21 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{+60} \\\Leftrightarrow & -420x-490x& = & 21+60 \\\Leftrightarrow & \color{red}{-910} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-910} & & \\\Leftrightarrow & x = \frac{-81}{910} & & \\ & V = \left\{ \frac{-81}{910} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{5})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -14x-\frac{28}{5}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-280}{ \color{blue}{20} }x- \frac{112}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -280x \color{red}{-112} & = & \color{red}{100x} +15 \\\Leftrightarrow & -280x \color{red}{-112} \color{blue}{+112} \color{blue}{-100x} & = & \color{red}{100x} +15 \color{blue}{-100x} \color{blue}{+112} \\\Leftrightarrow & -280x-100x& = & 15+112 \\\Leftrightarrow & \color{red}{-380} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-380} & & \\\Leftrightarrow & x = \frac{-127}{380} & & \\ & V = \left\{ \frac{-127}{380} \right\} & \\\end{align}\)