Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & 9x+\frac{2}{11} \\\Leftrightarrow & -4x+\frac{10}{11}& = & 9x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{+10} & = & \color{red}{99x} +2 \\\Leftrightarrow & -44x \color{red}{+10} \color{blue}{-10} \color{blue}{-99x} & = & \color{red}{99x} +2 \color{blue}{-99x} \color{blue}{-10} \\\Leftrightarrow & -44x-99x& = & 2-10 \\\Leftrightarrow & \color{red}{-143} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-143} & & \\\Leftrightarrow & x = \frac{8}{143} & & \\ & V = \left\{ \frac{8}{143} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{175x} +56 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -420x-175x& = & 56-150 \\\Leftrightarrow & \color{red}{-595} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{-595} & & \\\Leftrightarrow & x = \frac{94}{595} & & \\ & V = \left\{ \frac{94}{595} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{11})& = & -7x+\frac{5}{4} \\\Leftrightarrow & 6x+\frac{12}{11}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{264}{ \color{blue}{44} }x+ \frac{48}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 264x \color{red}{+48} & = & \color{red}{-308x} +55 \\\Leftrightarrow & 264x \color{red}{+48} \color{blue}{-48} \color{blue}{+308x} & = & \color{red}{-308x} +55 \color{blue}{+308x} \color{blue}{-48} \\\Leftrightarrow & 264x+308x& = & 55-48 \\\Leftrightarrow & \color{red}{572} x& = & 7 \\\Leftrightarrow & x = \frac{7}{572} & & \\ & V = \left\{ \frac{7}{572} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{9})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -12x+\frac{20}{9}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+100} & = & \color{red}{-225x} +72 \\\Leftrightarrow & -540x \color{red}{+100} \color{blue}{-100} \color{blue}{+225x} & = & \color{red}{-225x} +72 \color{blue}{+225x} \color{blue}{-100} \\\Leftrightarrow & -540x+225x& = & 72-100 \\\Leftrightarrow & \color{red}{-315} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-315} & & \\\Leftrightarrow & x = \frac{4}{45} & & \\ & V = \left\{ \frac{4}{45} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{5}{4})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{28}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{-45} & = & \color{red}{-84x} +28 \\\Leftrightarrow & -72x \color{red}{-45} \color{blue}{+45} \color{blue}{+84x} & = & \color{red}{-84x} +28 \color{blue}{+84x} \color{blue}{+45} \\\Leftrightarrow & -72x+84x& = & 28+45 \\\Leftrightarrow & \color{red}{12} x& = & 73 \\\Leftrightarrow & x = \frac{73}{12} & & \\ & V = \left\{ \frac{73}{12} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{9}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-18} & = & \color{red}{-70x} +25 \\\Leftrightarrow & -60x \color{red}{-18} \color{blue}{+18} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{+18} \\\Leftrightarrow & -60x+70x& = & 25+18 \\\Leftrightarrow & \color{red}{10} x& = & 43 \\\Leftrightarrow & x = \frac{43}{10} & & \\ & V = \left\{ \frac{43}{10} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{3})& = & -8x+\frac{5}{8} \\\Leftrightarrow & -15x-\frac{20}{3}& = & -8x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{-160} & = & \color{red}{-192x} +15 \\\Leftrightarrow & -360x \color{red}{-160} \color{blue}{+160} \color{blue}{+192x} & = & \color{red}{-192x} +15 \color{blue}{+192x} \color{blue}{+160} \\\Leftrightarrow & -360x+192x& = & 15+160 \\\Leftrightarrow & \color{red}{-168} x& = & 175 \\\Leftrightarrow & x = \frac{175}{-168} & & \\\Leftrightarrow & x = \frac{-25}{24} & & \\ & V = \left\{ \frac{-25}{24} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{147x} +28 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & -126x-147x& = & 28-18 \\\Leftrightarrow & \color{red}{-273} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-273} & & \\\Leftrightarrow & x = \frac{-10}{273} & & \\ & V = \left\{ \frac{-10}{273} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -9x+\frac{9}{8} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{448}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 448x \color{red}{+48} & = & \color{red}{-504x} +63 \\\Leftrightarrow & 448x \color{red}{+48} \color{blue}{-48} \color{blue}{+504x} & = & \color{red}{-504x} +63 \color{blue}{+504x} \color{blue}{-48} \\\Leftrightarrow & 448x+504x& = & 63-48 \\\Leftrightarrow & \color{red}{952} x& = & 15 \\\Leftrightarrow & x = \frac{15}{952} & & \\ & V = \left\{ \frac{15}{952} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{15}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+75} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -330x \color{red}{+75} \color{blue}{-75} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-75} \\\Leftrightarrow & -330x+385x& = & 66-75 \\\Leftrightarrow & \color{red}{55} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{55} & & \\ & V = \left\{ \frac{-9}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{-63x} +14 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{-30} \\\Leftrightarrow & 210x+63x& = & 14-30 \\\Leftrightarrow & \color{red}{273} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{273} & & \\ & V = \left\{ \frac{-16}{273} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{4})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -9x-\frac{15}{4}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-75} & = & \color{red}{-100x} +18 \\\Leftrightarrow & -180x \color{red}{-75} \color{blue}{+75} \color{blue}{+100x} & = & \color{red}{-100x} +18 \color{blue}{+100x} \color{blue}{+75} \\\Leftrightarrow & -180x+100x& = & 18+75 \\\Leftrightarrow & \color{red}{-80} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-80} & & \\\Leftrightarrow & x = \frac{-93}{80} & & \\ & V = \left\{ \frac{-93}{80} \right\} & \\\end{align}\)