Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{10})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 28x+\frac{21}{10}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3080}{ \color{blue}{110} }x+ \frac{231}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3080x \color{red}{+231} & = & \color{red}{-990x} +100 \\\Leftrightarrow & 3080x \color{red}{+231} \color{blue}{-231} \color{blue}{+990x} & = & \color{red}{-990x} +100 \color{blue}{+990x} \color{blue}{-231} \\\Leftrightarrow & 3080x+990x& = & 100-231 \\\Leftrightarrow & \color{red}{4070} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{4070} & & \\ & V = \left\{ \frac{-131}{4070} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{+54} \\\Leftrightarrow & -990x+693x& = & 88+54 \\\Leftrightarrow & \color{red}{-297} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-297} & & \\\Leftrightarrow & x = \frac{-142}{297} & & \\ & V = \left\{ \frac{-142}{297} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{5})& = & -3x+\frac{7}{10} \\\Leftrightarrow & 14x+\frac{14}{5}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{+28} & = & \color{red}{-30x} +7 \\\Leftrightarrow & 140x \color{red}{+28} \color{blue}{-28} \color{blue}{+30x} & = & \color{red}{-30x} +7 \color{blue}{+30x} \color{blue}{-28} \\\Leftrightarrow & 140x+30x& = & 7-28 \\\Leftrightarrow & \color{red}{170} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{8})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{-75} & = & \color{red}{280x} +64 \\\Leftrightarrow & 600x \color{red}{-75} \color{blue}{+75} \color{blue}{-280x} & = & \color{red}{280x} +64 \color{blue}{-280x} \color{blue}{+75} \\\Leftrightarrow & 600x-280x& = & 64+75 \\\Leftrightarrow & \color{red}{320} x& = & 139 \\\Leftrightarrow & x = \frac{139}{320} & & \\ & V = \left\{ \frac{139}{320} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{11})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 6x+\frac{12}{11}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{264}{ \color{blue}{44} }x+ \frac{48}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 264x \color{red}{+48} & = & \color{red}{220x} +55 \\\Leftrightarrow & 264x \color{red}{+48} \color{blue}{-48} \color{blue}{-220x} & = & \color{red}{220x} +55 \color{blue}{-220x} \color{blue}{-48} \\\Leftrightarrow & 264x-220x& = & 55-48 \\\Leftrightarrow & \color{red}{44} x& = & 7 \\\Leftrightarrow & x = \frac{7}{44} & & \\ & V = \left\{ \frac{7}{44} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{10}{11}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+30} & = & \color{red}{-99x} +44 \\\Leftrightarrow & 660x \color{red}{+30} \color{blue}{-30} \color{blue}{+99x} & = & \color{red}{-99x} +44 \color{blue}{+99x} \color{blue}{-30} \\\Leftrightarrow & 660x+99x& = & 44-30 \\\Leftrightarrow & \color{red}{759} x& = & 14 \\\Leftrightarrow & x = \frac{14}{759} & & \\ & V = \left\{ \frac{14}{759} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{6})& = & -8x+\frac{5}{11} \\\Leftrightarrow & -21x+\frac{35}{6}& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1386}{ \color{blue}{66} }x+ \frac{385}{ \color{blue}{66} })& = & (\frac{-528}{ \color{blue}{66} }x+ \frac{30}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1386x \color{red}{+385} & = & \color{red}{-528x} +30 \\\Leftrightarrow & -1386x \color{red}{+385} \color{blue}{-385} \color{blue}{+528x} & = & \color{red}{-528x} +30 \color{blue}{+528x} \color{blue}{-385} \\\Leftrightarrow & -1386x+528x& = & 30-385 \\\Leftrightarrow & \color{red}{-858} x& = & -355 \\\Leftrightarrow & x = \frac{-355}{-858} & & \\\Leftrightarrow & x = \frac{355}{858} & & \\ & V = \left\{ \frac{355}{858} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{11})& = & -2x+\frac{4}{11} \\\Leftrightarrow & 35x+\frac{35}{11}& = & -2x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{385}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 385x \color{red}{+35} & = & \color{red}{-22x} +4 \\\Leftrightarrow & 385x \color{red}{+35} \color{blue}{-35} \color{blue}{+22x} & = & \color{red}{-22x} +4 \color{blue}{+22x} \color{blue}{-35} \\\Leftrightarrow & 385x+22x& = & 4-35 \\\Leftrightarrow & \color{red}{407} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{407} & & \\ & V = \left\{ \frac{-31}{407} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{9})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -14x-\frac{28}{9}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-882}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -882x \color{red}{-196} & = & \color{red}{-315x} +81 \\\Leftrightarrow & -882x \color{red}{-196} \color{blue}{+196} \color{blue}{+315x} & = & \color{red}{-315x} +81 \color{blue}{+315x} \color{blue}{+196} \\\Leftrightarrow & -882x+315x& = & 81+196 \\\Leftrightarrow & \color{red}{-567} x& = & 277 \\\Leftrightarrow & x = \frac{277}{-567} & & \\\Leftrightarrow & x = \frac{-277}{567} & & \\ & V = \left\{ \frac{-277}{567} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{96x} +8 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +8 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & -180x-96x& = & 8-45 \\\Leftrightarrow & \color{red}{-276} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-276} & & \\\Leftrightarrow & x = \frac{37}{276} & & \\ & V = \left\{ \frac{37}{276} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x+ \frac{240}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{+240} & = & \color{red}{-280x} +49 \\\Leftrightarrow & -672x \color{red}{+240} \color{blue}{-240} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{-240} \\\Leftrightarrow & -672x+280x& = & 49-240 \\\Leftrightarrow & \color{red}{-392} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{-392} & & \\\Leftrightarrow & x = \frac{191}{392} & & \\ & V = \left\{ \frac{191}{392} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 4x+\frac{4}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-12} \\\Leftrightarrow & 60x+105x& = & 10-12 \\\Leftrightarrow & \color{red}{165} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{165} & & \\ & V = \left\{ \frac{-2}{165} \right\} & \\\end{align}\)