Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{8})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -21x+\frac{21}{8}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{+105} & = & \color{red}{320x} +16 \\\Leftrightarrow & -840x \color{red}{+105} \color{blue}{-105} \color{blue}{-320x} & = & \color{red}{320x} +16 \color{blue}{-320x} \color{blue}{-105} \\\Leftrightarrow & -840x-320x& = & 16-105 \\\Leftrightarrow & \color{red}{-1160} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-1160} & & \\\Leftrightarrow & x = \frac{89}{1160} & & \\ & V = \left\{ \frac{89}{1160} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{6})& = & -6x+\frac{10}{3} \\\Leftrightarrow & -35x+\frac{35}{6}& = & -6x+\frac{10}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-36}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{+35} & = & \color{red}{-36x} +20 \\\Leftrightarrow & -210x \color{red}{+35} \color{blue}{-35} \color{blue}{+36x} & = & \color{red}{-36x} +20 \color{blue}{+36x} \color{blue}{-35} \\\Leftrightarrow & -210x+36x& = & 20-35 \\\Leftrightarrow & \color{red}{-174} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-174} & & \\\Leftrightarrow & x = \frac{5}{58} & & \\ & V = \left\{ \frac{5}{58} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{11})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{6}{11}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+42} & = & \color{red}{-385x} +88 \\\Leftrightarrow & 924x \color{red}{+42} \color{blue}{-42} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{-42} \\\Leftrightarrow & 924x+385x& = & 88-42 \\\Leftrightarrow & \color{red}{1309} x& = & 46 \\\Leftrightarrow & x = \frac{46}{1309} & & \\ & V = \left\{ \frac{46}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1120}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1120x \color{red}{+105} & = & \color{red}{200x} +16 \\\Leftrightarrow & 1120x \color{red}{+105} \color{blue}{-105} \color{blue}{-200x} & = & \color{red}{200x} +16 \color{blue}{-200x} \color{blue}{-105} \\\Leftrightarrow & 1120x-200x& = & 16-105 \\\Leftrightarrow & \color{red}{920} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{920} & & \\ & V = \left\{ \frac{-89}{920} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{4})& = & -6x+\frac{3}{8} \\\Leftrightarrow & 25x+\frac{25}{4}& = & -6x+\frac{3}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{200}{ \color{blue}{8} }x+ \frac{50}{ \color{blue}{8} })& = & (\frac{-48}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 200x \color{red}{+50} & = & \color{red}{-48x} +3 \\\Leftrightarrow & 200x \color{red}{+50} \color{blue}{-50} \color{blue}{+48x} & = & \color{red}{-48x} +3 \color{blue}{+48x} \color{blue}{-50} \\\Leftrightarrow & 200x+48x& = & 3-50 \\\Leftrightarrow & \color{red}{248} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{248} & & \\ & V = \left\{ \frac{-47}{248} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -4x-\frac{6}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{-6} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -44x \color{red}{-6} \color{blue}{+6} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{+6} \\\Leftrightarrow & -44x+99x& = & 6+6 \\\Leftrightarrow & \color{red}{55} x& = & 12 \\\Leftrightarrow & x = \frac{12}{55} & & \\ & V = \left\{ \frac{12}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 18x-\frac{30}{11}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{-270} & = & \color{red}{495x} +44 \\\Leftrightarrow & 1782x \color{red}{-270} \color{blue}{+270} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{+270} \\\Leftrightarrow & 1782x-495x& = & 44+270 \\\Leftrightarrow & \color{red}{1287} x& = & 314 \\\Leftrightarrow & x = \frac{314}{1287} & & \\ & V = \left\{ \frac{314}{1287} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{10})& = & 7x+\frac{7}{11} \\\Leftrightarrow & -6x-\frac{9}{10}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-660}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{70}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -660x \color{red}{-99} & = & \color{red}{770x} +70 \\\Leftrightarrow & -660x \color{red}{-99} \color{blue}{+99} \color{blue}{-770x} & = & \color{red}{770x} +70 \color{blue}{-770x} \color{blue}{+99} \\\Leftrightarrow & -660x-770x& = & 70+99 \\\Leftrightarrow & \color{red}{-1430} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-1430} & & \\\Leftrightarrow & x = \frac{-13}{110} & & \\ & V = \left\{ \frac{-13}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{20}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{100}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-100} & = & \color{red}{385x} +66 \\\Leftrightarrow & -550x \color{red}{-100} \color{blue}{+100} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+100} \\\Leftrightarrow & -550x-385x& = & 66+100 \\\Leftrightarrow & \color{red}{-935} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-935} & & \\\Leftrightarrow & x = \frac{-166}{935} & & \\ & V = \left\{ \frac{-166}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-88} & = & \color{red}{-231x} +30 \\\Leftrightarrow & -330x \color{red}{-88} \color{blue}{+88} \color{blue}{+231x} & = & \color{red}{-231x} +30 \color{blue}{+231x} \color{blue}{+88} \\\Leftrightarrow & -330x+231x& = & 30+88 \\\Leftrightarrow & \color{red}{-99} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-99} & & \\\Leftrightarrow & x = \frac{-118}{99} & & \\ & V = \left\{ \frac{-118}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{11})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 6x-\frac{6}{11}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{-6} & = & \color{red}{55x} +7 \\\Leftrightarrow & 66x \color{red}{-6} \color{blue}{+6} \color{blue}{-55x} & = & \color{red}{55x} +7 \color{blue}{-55x} \color{blue}{+6} \\\Leftrightarrow & 66x-55x& = & 7+6 \\\Leftrightarrow & \color{red}{11} x& = & 13 \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 12x-\frac{6}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-12} & = & \color{red}{110x} +55 \\\Leftrightarrow & 264x \color{red}{-12} \color{blue}{+12} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{+12} \\\Leftrightarrow & 264x-110x& = & 55+12 \\\Leftrightarrow & \color{red}{154} x& = & 67 \\\Leftrightarrow & x = \frac{67}{154} & & \\ & V = \left\{ \frac{67}{154} \right\} & \\\end{align}\)