Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+150} & = & \color{red}{245x} +63 \\\Leftrightarrow & -840x \color{red}{+150} \color{blue}{-150} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{-150} \\\Leftrightarrow & -840x-245x& = & 63-150 \\\Leftrightarrow & \color{red}{-1085} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-1085} & & \\\Leftrightarrow & x = \frac{87}{1085} & & \\ & V = \left\{ \frac{87}{1085} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{147x} +70 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & -336x-147x& = & 70+48 \\\Leftrightarrow & \color{red}{-483} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-483} & & \\\Leftrightarrow & x = \frac{-118}{483} & & \\ & V = \left\{ \frac{-118}{483} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -8x+\frac{3}{10} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+24} & = & \color{red}{-80x} +3 \\\Leftrightarrow & -150x \color{red}{+24} \color{blue}{-24} \color{blue}{+80x} & = & \color{red}{-80x} +3 \color{blue}{+80x} \color{blue}{-24} \\\Leftrightarrow & -150x+80x& = & 3-24 \\\Leftrightarrow & \color{red}{-70} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-70} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{9}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+18} & = & \color{red}{-50x} +45 \\\Leftrightarrow & 60x \color{red}{+18} \color{blue}{-18} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{-18} \\\Leftrightarrow & 60x+50x& = & 45-18 \\\Leftrightarrow & \color{red}{110} x& = & 27 \\\Leftrightarrow & x = \frac{27}{110} & & \\ & V = \left\{ \frac{27}{110} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{11})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -21x-\frac{21}{11}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-63} & = & \color{red}{264x} +44 \\\Leftrightarrow & -693x \color{red}{-63} \color{blue}{+63} \color{blue}{-264x} & = & \color{red}{264x} +44 \color{blue}{-264x} \color{blue}{+63} \\\Leftrightarrow & -693x-264x& = & 44+63 \\\Leftrightarrow & \color{red}{-957} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-957} & & \\\Leftrightarrow & x = \frac{-107}{957} & & \\ & V = \left\{ \frac{-107}{957} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{11})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{15}{11}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-30} & = & \color{red}{-110x} +55 \\\Leftrightarrow & -264x \color{red}{-30} \color{blue}{+30} \color{blue}{+110x} & = & \color{red}{-110x} +55 \color{blue}{+110x} \color{blue}{+30} \\\Leftrightarrow & -264x+110x& = & 55+30 \\\Leftrightarrow & \color{red}{-154} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-154} & & \\\Leftrightarrow & x = \frac{-85}{154} & & \\ & V = \left\{ \frac{-85}{154} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 16x+\frac{12}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{+108} & = & \color{red}{495x} +110 \\\Leftrightarrow & 1584x \color{red}{+108} \color{blue}{-108} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{-108} \\\Leftrightarrow & 1584x-495x& = & 110-108 \\\Leftrightarrow & \color{red}{1089} x& = & 2 \\\Leftrightarrow & x = \frac{2}{1089} & & \\ & V = \left\{ \frac{2}{1089} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -126x+147x& = & 70+18 \\\Leftrightarrow & \color{red}{21} x& = & 88 \\\Leftrightarrow & x = \frac{88}{21} & & \\ & V = \left\{ \frac{88}{21} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{7})& = & 9x+\frac{9}{11} \\\Leftrightarrow & 20x+\frac{15}{7}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+165} & = & \color{red}{693x} +63 \\\Leftrightarrow & 1540x \color{red}{+165} \color{blue}{-165} \color{blue}{-693x} & = & \color{red}{693x} +63 \color{blue}{-693x} \color{blue}{-165} \\\Leftrightarrow & 1540x-693x& = & 63-165 \\\Leftrightarrow & \color{red}{847} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{847} & & \\ & V = \left\{ \frac{-102}{847} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{9})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 8x+\frac{16}{9}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x+ \frac{32}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+32} & = & \color{red}{-90x} +21 \\\Leftrightarrow & 144x \color{red}{+32} \color{blue}{-32} \color{blue}{+90x} & = & \color{red}{-90x} +21 \color{blue}{+90x} \color{blue}{-32} \\\Leftrightarrow & 144x+90x& = & 21-32 \\\Leftrightarrow & \color{red}{234} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{234} & & \\ & V = \left\{ \frac{-11}{234} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & 9x+\frac{8}{11} \\\Leftrightarrow & -35x-\frac{28}{9}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-308} & = & \color{red}{891x} +72 \\\Leftrightarrow & -3465x \color{red}{-308} \color{blue}{+308} \color{blue}{-891x} & = & \color{red}{891x} +72 \color{blue}{-891x} \color{blue}{+308} \\\Leftrightarrow & -3465x-891x& = & 72+308 \\\Leftrightarrow & \color{red}{-4356} x& = & 380 \\\Leftrightarrow & x = \frac{380}{-4356} & & \\\Leftrightarrow & x = \frac{-95}{1089} & & \\ & V = \left\{ \frac{-95}{1089} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{8}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+56} & = & \color{red}{539x} +99 \\\Leftrightarrow & -462x \color{red}{+56} \color{blue}{-56} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{-56} \\\Leftrightarrow & -462x-539x& = & 99-56 \\\Leftrightarrow & \color{red}{-1001} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-1001} & & \\\Leftrightarrow & x = \frac{-43}{1001} & & \\ & V = \left\{ \frac{-43}{1001} \right\} & \\\end{align}\)