Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{30}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-30} & = & \color{red}{77x} +6 \\\Leftrightarrow & 132x \color{red}{-30} \color{blue}{+30} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{+30} \\\Leftrightarrow & 132x-77x& = & 6+30 \\\Leftrightarrow & \color{red}{55} x& = & 36 \\\Leftrightarrow & x = \frac{36}{55} & & \\ & V = \left\{ \frac{36}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{3})& = & 8x+\frac{8}{11} \\\Leftrightarrow & -25x-\frac{20}{3}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-220} & = & \color{red}{264x} +24 \\\Leftrightarrow & -825x \color{red}{-220} \color{blue}{+220} \color{blue}{-264x} & = & \color{red}{264x} +24 \color{blue}{-264x} \color{blue}{+220} \\\Leftrightarrow & -825x-264x& = & 24+220 \\\Leftrightarrow & \color{red}{-1089} x& = & 244 \\\Leftrightarrow & x = \frac{244}{-1089} & & \\\Leftrightarrow & x = \frac{-244}{1089} & & \\ & V = \left\{ \frac{-244}{1089} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-88} & = & \color{red}{-495x} +54 \\\Leftrightarrow & 792x \color{red}{-88} \color{blue}{+88} \color{blue}{+495x} & = & \color{red}{-495x} +54 \color{blue}{+495x} \color{blue}{+88} \\\Leftrightarrow & 792x+495x& = & 54+88 \\\Leftrightarrow & \color{red}{1287} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1287} & & \\ & V = \left\{ \frac{142}{1287} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & 2x+\frac{4}{5} \\\Leftrightarrow & 9x-\frac{6}{11}& = & 2x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-30} & = & \color{red}{110x} +44 \\\Leftrightarrow & 495x \color{red}{-30} \color{blue}{+30} \color{blue}{-110x} & = & \color{red}{110x} +44 \color{blue}{-110x} \color{blue}{+30} \\\Leftrightarrow & 495x-110x& = & 44+30 \\\Leftrightarrow & \color{red}{385} x& = & 74 \\\Leftrightarrow & x = \frac{74}{385} & & \\ & V = \left\{ \frac{74}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{11})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{25}{11}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{125}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-125} & = & \color{red}{-385x} +44 \\\Leftrightarrow & 825x \color{red}{-125} \color{blue}{+125} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+125} \\\Leftrightarrow & 825x+385x& = & 44+125 \\\Leftrightarrow & \color{red}{1210} x& = & 169 \\\Leftrightarrow & x = \frac{169}{1210} & & \\ & V = \left\{ \frac{169}{1210} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{8})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{15}{8}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-528}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -528x \color{red}{+165} & = & \color{red}{-616x} +16 \\\Leftrightarrow & -528x \color{red}{+165} \color{blue}{-165} \color{blue}{+616x} & = & \color{red}{-616x} +16 \color{blue}{+616x} \color{blue}{-165} \\\Leftrightarrow & -528x+616x& = & 16-165 \\\Leftrightarrow & \color{red}{88} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{88} & & \\ & V = \left\{ \frac{-149}{88} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{7})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-336}{ \color{blue}{84} }x- \frac{72}{ \color{blue}{84} })& = & (\frac{-420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -336x \color{red}{-72} & = & \color{red}{-420x} +35 \\\Leftrightarrow & -336x \color{red}{-72} \color{blue}{+72} \color{blue}{+420x} & = & \color{red}{-420x} +35 \color{blue}{+420x} \color{blue}{+72} \\\Leftrightarrow & -336x+420x& = & 35+72 \\\Leftrightarrow & \color{red}{84} x& = & 107 \\\Leftrightarrow & x = \frac{107}{84} & & \\ & V = \left\{ \frac{107}{84} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{4})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{360}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 360x \color{red}{+135} & = & \color{red}{-252x} +32 \\\Leftrightarrow & 360x \color{red}{+135} \color{blue}{-135} \color{blue}{+252x} & = & \color{red}{-252x} +32 \color{blue}{+252x} \color{blue}{-135} \\\Leftrightarrow & 360x+252x& = & 32-135 \\\Leftrightarrow & \color{red}{612} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{612} & & \\ & V = \left\{ \frac{-103}{612} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{3})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 20x-\frac{8}{3}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{-40} & = & \color{red}{105x} +6 \\\Leftrightarrow & 300x \color{red}{-40} \color{blue}{+40} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{+40} \\\Leftrightarrow & 300x-105x& = & 6+40 \\\Leftrightarrow & \color{red}{195} x& = & 46 \\\Leftrightarrow & x = \frac{46}{195} & & \\ & V = \left\{ \frac{46}{195} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{9})& = & -3x+\frac{9}{8} \\\Leftrightarrow & -14x+\frac{14}{9}& = & -3x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x+ \frac{112}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{+112} & = & \color{red}{-216x} +81 \\\Leftrightarrow & -1008x \color{red}{+112} \color{blue}{-112} \color{blue}{+216x} & = & \color{red}{-216x} +81 \color{blue}{+216x} \color{blue}{-112} \\\Leftrightarrow & -1008x+216x& = & 81-112 \\\Leftrightarrow & \color{red}{-792} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-792} & & \\\Leftrightarrow & x = \frac{31}{792} & & \\ & V = \left\{ \frac{31}{792} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{9})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -16x+\frac{8}{9}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+56} & = & \color{red}{441x} +36 \\\Leftrightarrow & -1008x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +36 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & -1008x-441x& = & 36-56 \\\Leftrightarrow & \color{red}{-1449} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-1449} & & \\\Leftrightarrow & x = \frac{20}{1449} & & \\ & V = \left\{ \frac{20}{1449} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-360}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -360x \color{red}{+32} & = & \color{red}{252x} +63 \\\Leftrightarrow & -360x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +63 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & -360x-252x& = & 63-32 \\\Leftrightarrow & \color{red}{-612} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-612} & & \\\Leftrightarrow & x = \frac{-31}{612} & & \\ & V = \left\{ \frac{-31}{612} \right\} & \\\end{align}\)