Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 9x+\frac{2}{11} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 9x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-66} & = & \color{red}{693x} +14 \\\Leftrightarrow & -308x \color{red}{-66} \color{blue}{+66} \color{blue}{-693x} & = & \color{red}{693x} +14 \color{blue}{-693x} \color{blue}{+66} \\\Leftrightarrow & -308x-693x& = & 14+66 \\\Leftrightarrow & \color{red}{-1001} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-1001} & & \\\Leftrightarrow & x = \frac{-80}{1001} & & \\ & V = \left\{ \frac{-80}{1001} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{3})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 20x+\frac{10}{3}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+50} & = & \color{red}{105x} +12 \\\Leftrightarrow & 300x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & 300x-105x& = & 12-50 \\\Leftrightarrow & \color{red}{195} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{195} & & \\ & V = \left\{ \frac{-38}{195} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{3})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+14} & = & \color{red}{-24x} +8 \\\Leftrightarrow & -63x \color{red}{+14} \color{blue}{-14} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{-14} \\\Leftrightarrow & -63x+24x& = & 8-14 \\\Leftrightarrow & \color{red}{-39} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-39} & & \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{11})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 28x+\frac{28}{11}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{616}{ \color{blue}{22} }x+ \frac{56}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 616x \color{red}{+56} & = & \color{red}{-66x} +55 \\\Leftrightarrow & 616x \color{red}{+56} \color{blue}{-56} \color{blue}{+66x} & = & \color{red}{-66x} +55 \color{blue}{+66x} \color{blue}{-56} \\\Leftrightarrow & 616x+66x& = & 55-56 \\\Leftrightarrow & \color{red}{682} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{682} & & \\ & V = \left\{ \frac{-1}{682} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{20}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-220} & = & \color{red}{539x} +42 \\\Leftrightarrow & 616x \color{red}{-220} \color{blue}{+220} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+220} \\\Leftrightarrow & 616x-539x& = & 42+220 \\\Leftrightarrow & \color{red}{77} x& = & 262 \\\Leftrightarrow & x = \frac{262}{77} & & \\ & V = \left\{ \frac{262}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{5})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+4} & = & \color{red}{-45x} +8 \\\Leftrightarrow & -40x \color{red}{+4} \color{blue}{-4} \color{blue}{+45x} & = & \color{red}{-45x} +8 \color{blue}{+45x} \color{blue}{-4} \\\Leftrightarrow & -40x+45x& = & 8-4 \\\Leftrightarrow & \color{red}{5} x& = & 4 \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{-108} & = & \color{red}{315x} +40 \\\Leftrightarrow & -900x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & -900x-315x& = & 40+108 \\\Leftrightarrow & \color{red}{-1215} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-1215} & & \\\Leftrightarrow & x = \frac{-148}{1215} & & \\ & V = \left\{ \frac{-148}{1215} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 28x-\frac{35}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-105} & = & \color{red}{165x} +88 \\\Leftrightarrow & 924x \color{red}{-105} \color{blue}{+105} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+105} \\\Leftrightarrow & 924x-165x& = & 88+105 \\\Leftrightarrow & \color{red}{759} x& = & 193 \\\Leftrightarrow & x = \frac{193}{759} & & \\ & V = \left\{ \frac{193}{759} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{11})& = & -3x+\frac{9}{7} \\\Leftrightarrow & -8x+\frac{4}{11}& = & -3x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+28} & = & \color{red}{-231x} +99 \\\Leftrightarrow & -616x \color{red}{+28} \color{blue}{-28} \color{blue}{+231x} & = & \color{red}{-231x} +99 \color{blue}{+231x} \color{blue}{-28} \\\Leftrightarrow & -616x+231x& = & 99-28 \\\Leftrightarrow & \color{red}{-385} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-385} & & \\\Leftrightarrow & x = \frac{-71}{385} & & \\ & V = \left\{ \frac{-71}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -6x-\frac{6}{5}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-66} & = & \color{red}{-385x} +40 \\\Leftrightarrow & -330x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +40 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & -330x+385x& = & 40+66 \\\Leftrightarrow & \color{red}{55} x& = & 106 \\\Leftrightarrow & x = \frac{106}{55} & & \\ & V = \left\{ \frac{106}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 660x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{1045} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1045} & & \\ & V = \left\{ \frac{162}{1045} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+36} & = & \color{red}{30x} +10 \\\Leftrightarrow & 225x \color{red}{+36} \color{blue}{-36} \color{blue}{-30x} & = & \color{red}{30x} +10 \color{blue}{-30x} \color{blue}{-36} \\\Leftrightarrow & 225x-30x& = & 10-36 \\\Leftrightarrow & \color{red}{195} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{195} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)