Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{11})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -24x+\frac{24}{11}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{275x} +44 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-275x} & = & \color{red}{275x} +44 \color{blue}{-275x} \color{blue}{-120} \\\Leftrightarrow & -1320x-275x& = & 44-120 \\\Leftrightarrow & \color{red}{-1595} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-1595} & & \\\Leftrightarrow & x = \frac{76}{1595} & & \\ & V = \left\{ \frac{76}{1595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2640}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2640x \color{red}{+180} & = & \color{red}{770x} +77 \\\Leftrightarrow & -2640x \color{red}{+180} \color{blue}{-180} \color{blue}{-770x} & = & \color{red}{770x} +77 \color{blue}{-770x} \color{blue}{-180} \\\Leftrightarrow & -2640x-770x& = & 77-180 \\\Leftrightarrow & \color{red}{-3410} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-3410} & & \\\Leftrightarrow & x = \frac{103}{3410} & & \\ & V = \left\{ \frac{103}{3410} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{+18} & = & \color{red}{147x} +14 \\\Leftrightarrow & 189x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & 189x-147x& = & 14-18 \\\Leftrightarrow & \color{red}{42} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{42} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -16x+\frac{20}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+220} & = & \color{red}{-693x} +45 \\\Leftrightarrow & -1584x \color{red}{+220} \color{blue}{-220} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{-220} \\\Leftrightarrow & -1584x+693x& = & 45-220 \\\Leftrightarrow & \color{red}{-891} x& = & -175 \\\Leftrightarrow & x = \frac{-175}{-891} & & \\\Leftrightarrow & x = \frac{175}{891} & & \\ & V = \left\{ \frac{175}{891} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{5})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+108} & = & \color{red}{-405x} +40 \\\Leftrightarrow & 360x \color{red}{+108} \color{blue}{-108} \color{blue}{+405x} & = & \color{red}{-405x} +40 \color{blue}{+405x} \color{blue}{-108} \\\Leftrightarrow & 360x+405x& = & 40-108 \\\Leftrightarrow & \color{red}{765} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{765} & & \\\Leftrightarrow & x = \frac{-4}{45} & & \\ & V = \left\{ \frac{-4}{45} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{1}{3})& = & -8x+\frac{5}{3} \\\Leftrightarrow & -21x+\frac{7}{3}& = & -8x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+7} & = & \color{red}{-24x} +5 \\\Leftrightarrow & -63x \color{red}{+7} \color{blue}{-7} \color{blue}{+24x} & = & \color{red}{-24x} +5 \color{blue}{+24x} \color{blue}{-7} \\\Leftrightarrow & -63x+24x& = & 5-7 \\\Leftrightarrow & \color{red}{-39} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-39} & & \\\Leftrightarrow & x = \frac{2}{39} & & \\ & V = \left\{ \frac{2}{39} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-108} & = & \color{red}{405x} +20 \\\Leftrightarrow & 360x \color{red}{-108} \color{blue}{+108} \color{blue}{-405x} & = & \color{red}{405x} +20 \color{blue}{-405x} \color{blue}{+108} \\\Leftrightarrow & 360x-405x& = & 20+108 \\\Leftrightarrow & \color{red}{-45} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-45} & & \\\Leftrightarrow & x = \frac{-128}{45} & & \\ & V = \left\{ \frac{-128}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+10} & = & \color{red}{-49x} +5 \\\Leftrightarrow & -42x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +5 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -42x+49x& = & 5-10 \\\Leftrightarrow & \color{red}{7} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1200}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1200x \color{red}{+96} & = & \color{red}{280x} +15 \\\Leftrightarrow & -1200x \color{red}{+96} \color{blue}{-96} \color{blue}{-280x} & = & \color{red}{280x} +15 \color{blue}{-280x} \color{blue}{-96} \\\Leftrightarrow & -1200x-280x& = & 15-96 \\\Leftrightarrow & \color{red}{-1480} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-1480} & & \\\Leftrightarrow & x = \frac{81}{1480} & & \\ & V = \left\{ \frac{81}{1480} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{+16} & = & \color{red}{63x} +10 \\\Leftrightarrow & 112x \color{red}{+16} \color{blue}{-16} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-16} \\\Leftrightarrow & 112x-63x& = & 10-16 \\\Leftrightarrow & \color{red}{49} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{49} & & \\ & V = \left\{ \frac{-6}{49} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 12x-\frac{18}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-18} & = & \color{red}{-55x} +4 \\\Leftrightarrow & 132x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & 132x+55x& = & 4+18 \\\Leftrightarrow & \color{red}{187} x& = & 22 \\\Leftrightarrow & x = \frac{22}{187} & & \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{-147x} +15 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{+147x} & = & \color{red}{-147x} +15 \color{blue}{+147x} \color{blue}{-140} \\\Leftrightarrow & 420x+147x& = & 15-140 \\\Leftrightarrow & \color{red}{567} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{567} & & \\ & V = \left\{ \frac{-125}{567} \right\} & \\\end{align}\)