Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{8}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-24} & = & \color{red}{231x} +22 \\\Leftrightarrow & -330x \color{red}{-24} \color{blue}{+24} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+24} \\\Leftrightarrow & -330x-231x& = & 22+24 \\\Leftrightarrow & \color{red}{-561} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-561} & & \\\Leftrightarrow & x = \frac{-46}{561} & & \\ & V = \left\{ \frac{-46}{561} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{11})& = & 3x+\frac{9}{8} \\\Leftrightarrow & 16x+\frac{8}{11}& = & 3x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1408}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1408x \color{red}{+64} & = & \color{red}{264x} +99 \\\Leftrightarrow & 1408x \color{red}{+64} \color{blue}{-64} \color{blue}{-264x} & = & \color{red}{264x} +99 \color{blue}{-264x} \color{blue}{-64} \\\Leftrightarrow & 1408x-264x& = & 99-64 \\\Leftrightarrow & \color{red}{1144} x& = & 35 \\\Leftrightarrow & x = \frac{35}{1144} & & \\ & V = \left\{ \frac{35}{1144} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{-105x} +20 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{-72} \\\Leftrightarrow & 450x+105x& = & 20-72 \\\Leftrightarrow & \color{red}{555} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{555} & & \\ & V = \left\{ \frac{-52}{555} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 14x+\frac{14}{3}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{112}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+112} & = & \color{red}{72x} +21 \\\Leftrightarrow & 336x \color{red}{+112} \color{blue}{-112} \color{blue}{-72x} & = & \color{red}{72x} +21 \color{blue}{-72x} \color{blue}{-112} \\\Leftrightarrow & 336x-72x& = & 21-112 \\\Leftrightarrow & \color{red}{264} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{264} & & \\ & V = \left\{ \frac{-91}{264} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-8} & = & \color{red}{90x} +35 \\\Leftrightarrow & 80x \color{red}{-8} \color{blue}{+8} \color{blue}{-90x} & = & \color{red}{90x} +35 \color{blue}{-90x} \color{blue}{+8} \\\Leftrightarrow & 80x-90x& = & 35+8 \\\Leftrightarrow & \color{red}{-10} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-10} & & \\\Leftrightarrow & x = \frac{-43}{10} & & \\ & V = \left\{ \frac{-43}{10} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{11})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 8x-\frac{16}{11}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-80} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 440x \color{red}{-80} \color{blue}{+80} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+80} \\\Leftrightarrow & 440x+165x& = & 88+80 \\\Leftrightarrow & \color{red}{605} x& = & 168 \\\Leftrightarrow & x = \frac{168}{605} & & \\ & V = \left\{ \frac{168}{605} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{1}{3})& = & -2x+\frac{7}{8} \\\Leftrightarrow & 35x-\frac{7}{3}& = & -2x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{840}{ \color{blue}{24} }x- \frac{56}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 840x \color{red}{-56} & = & \color{red}{-48x} +21 \\\Leftrightarrow & 840x \color{red}{-56} \color{blue}{+56} \color{blue}{+48x} & = & \color{red}{-48x} +21 \color{blue}{+48x} \color{blue}{+56} \\\Leftrightarrow & 840x+48x& = & 21+56 \\\Leftrightarrow & \color{red}{888} x& = & 77 \\\Leftrightarrow & x = \frac{77}{888} & & \\ & V = \left\{ \frac{77}{888} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{8})& = & 4x+\frac{7}{2} \\\Leftrightarrow & 9x-\frac{15}{8}& = & 4x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{32}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{-15} & = & \color{red}{32x} +28 \\\Leftrightarrow & 72x \color{red}{-15} \color{blue}{+15} \color{blue}{-32x} & = & \color{red}{32x} +28 \color{blue}{-32x} \color{blue}{+15} \\\Leftrightarrow & 72x-32x& = & 28+15 \\\Leftrightarrow & \color{red}{40} x& = & 43 \\\Leftrightarrow & x = \frac{43}{40} & & \\ & V = \left\{ \frac{43}{40} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{7})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{12}{7}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+36} & = & \color{red}{-168x} +28 \\\Leftrightarrow & -315x \color{red}{+36} \color{blue}{-36} \color{blue}{+168x} & = & \color{red}{-168x} +28 \color{blue}{+168x} \color{blue}{-36} \\\Leftrightarrow & -315x+168x& = & 28-36 \\\Leftrightarrow & \color{red}{-147} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-147} & & \\\Leftrightarrow & x = \frac{8}{147} & & \\ & V = \left\{ \frac{8}{147} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{4})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -28x+\frac{35}{4}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-560}{ \color{blue}{20} }x+ \frac{175}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -560x \color{red}{+175} & = & \color{red}{-180x} +24 \\\Leftrightarrow & -560x \color{red}{+175} \color{blue}{-175} \color{blue}{+180x} & = & \color{red}{-180x} +24 \color{blue}{+180x} \color{blue}{-175} \\\Leftrightarrow & -560x+180x& = & 24-175 \\\Leftrightarrow & \color{red}{-380} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{-380} & & \\\Leftrightarrow & x = \frac{151}{380} & & \\ & V = \left\{ \frac{151}{380} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+18} & = & \color{red}{99x} +44 \\\Leftrightarrow & 330x \color{red}{+18} \color{blue}{-18} \color{blue}{-99x} & = & \color{red}{99x} +44 \color{blue}{-99x} \color{blue}{-18} \\\Leftrightarrow & 330x-99x& = & 44-18 \\\Leftrightarrow & \color{red}{231} x& = & 26 \\\Leftrightarrow & x = \frac{26}{231} & & \\ & V = \left\{ \frac{26}{231} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{12})& = & -8x+\frac{8}{3} \\\Leftrightarrow & 25x-\frac{25}{12}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{-25} & = & \color{red}{-96x} +32 \\\Leftrightarrow & 300x \color{red}{-25} \color{blue}{+25} \color{blue}{+96x} & = & \color{red}{-96x} +32 \color{blue}{+96x} \color{blue}{+25} \\\Leftrightarrow & 300x+96x& = & 32+25 \\\Leftrightarrow & \color{red}{396} x& = & 57 \\\Leftrightarrow & x = \frac{57}{396} & & \\\Leftrightarrow & x = \frac{19}{132} & & \\ & V = \left\{ \frac{19}{132} \right\} & \\\end{align}\)