Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{6}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+18} \\\Leftrightarrow & 120x+75x& = & 50+18 \\\Leftrightarrow & \color{red}{195} x& = & 68 \\\Leftrightarrow & x = \frac{68}{195} & & \\ & V = \left\{ \frac{68}{195} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{20}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-220} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 924x \color{red}{-220} \color{blue}{+220} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+220} \\\Leftrightarrow & 924x+539x& = & 42+220 \\\Leftrightarrow & \color{red}{1463} x& = & 262 \\\Leftrightarrow & x = \frac{262}{1463} & & \\ & V = \left\{ \frac{262}{1463} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & 2x+\frac{9}{10} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{40}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{40x} +18 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{-40x} & = & \color{red}{40x} +18 \color{blue}{-40x} \color{blue}{+75} \\\Leftrightarrow & 300x-40x& = & 18+75 \\\Leftrightarrow & \color{red}{260} x& = & 93 \\\Leftrightarrow & x = \frac{93}{260} & & \\ & V = \left\{ \frac{93}{260} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{2})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{25}{2}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-75} & = & \color{red}{-18x} +4 \\\Leftrightarrow & 120x \color{red}{-75} \color{blue}{+75} \color{blue}{+18x} & = & \color{red}{-18x} +4 \color{blue}{+18x} \color{blue}{+75} \\\Leftrightarrow & 120x+18x& = & 4+75 \\\Leftrightarrow & \color{red}{138} x& = & 79 \\\Leftrightarrow & x = \frac{79}{138} & & \\ & V = \left\{ \frac{79}{138} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & 3x+\frac{3}{8} \\\Leftrightarrow & 4x+\frac{10}{11}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{352}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 352x \color{red}{+80} & = & \color{red}{264x} +33 \\\Leftrightarrow & 352x \color{red}{+80} \color{blue}{-80} \color{blue}{-264x} & = & \color{red}{264x} +33 \color{blue}{-264x} \color{blue}{-80} \\\Leftrightarrow & 352x-264x& = & 33-80 \\\Leftrightarrow & \color{red}{88} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{88} & & \\ & V = \left\{ \frac{-47}{88} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{3})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{10}{3}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-70} & = & \color{red}{-147x} +6 \\\Leftrightarrow & 168x \color{red}{-70} \color{blue}{+70} \color{blue}{+147x} & = & \color{red}{-147x} +6 \color{blue}{+147x} \color{blue}{+70} \\\Leftrightarrow & 168x+147x& = & 6+70 \\\Leftrightarrow & \color{red}{315} x& = & 76 \\\Leftrightarrow & x = \frac{76}{315} & & \\ & V = \left\{ \frac{76}{315} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{11})& = & -9x+\frac{9}{11} \\\Leftrightarrow & 8x+\frac{6}{11}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{+6} & = & \color{red}{-99x} +9 \\\Leftrightarrow & 88x \color{red}{+6} \color{blue}{-6} \color{blue}{+99x} & = & \color{red}{-99x} +9 \color{blue}{+99x} \color{blue}{-6} \\\Leftrightarrow & 88x+99x& = & 9-6 \\\Leftrightarrow & \color{red}{187} x& = & 3 \\\Leftrightarrow & x = \frac{3}{187} & & \\ & V = \left\{ \frac{3}{187} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-30} \\\Leftrightarrow & 420x+175x& = & 28-30 \\\Leftrightarrow & \color{red}{595} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{595} & & \\ & V = \left\{ \frac{-2}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-126} & = & \color{red}{175x} +45 \\\Leftrightarrow & -840x \color{red}{-126} \color{blue}{+126} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{+126} \\\Leftrightarrow & -840x-175x& = & 45+126 \\\Leftrightarrow & \color{red}{-1015} x& = & 171 \\\Leftrightarrow & x = \frac{171}{-1015} & & \\\Leftrightarrow & x = \frac{-171}{1015} & & \\ & V = \left\{ \frac{-171}{1015} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{10})& = & 2x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{9}{10}& = & 2x+\frac{2}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1350}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} })& = & (\frac{180}{ \color{blue}{90} }x+ \frac{20}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1350x \color{red}{+81} & = & \color{red}{180x} +20 \\\Leftrightarrow & 1350x \color{red}{+81} \color{blue}{-81} \color{blue}{-180x} & = & \color{red}{180x} +20 \color{blue}{-180x} \color{blue}{-81} \\\Leftrightarrow & 1350x-180x& = & 20-81 \\\Leftrightarrow & \color{red}{1170} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{1170} & & \\ & V = \left\{ \frac{-61}{1170} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{3})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+60} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 180x \color{red}{+60} \color{blue}{-60} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{-60} \\\Leftrightarrow & 180x+27x& = & 8-60 \\\Leftrightarrow & \color{red}{207} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{207} & & \\ & V = \left\{ \frac{-52}{207} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-504}{ \color{blue}{84} }x- \frac{72}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -504x \color{red}{-72} & = & \color{red}{588x} +49 \\\Leftrightarrow & -504x \color{red}{-72} \color{blue}{+72} \color{blue}{-588x} & = & \color{red}{588x} +49 \color{blue}{-588x} \color{blue}{+72} \\\Leftrightarrow & -504x-588x& = & 49+72 \\\Leftrightarrow & \color{red}{-1092} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-1092} & & \\\Leftrightarrow & x = \frac{-121}{1092} & & \\ & V = \left\{ \frac{-121}{1092} \right\} & \\\end{align}\)