Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{4})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -10x-\frac{15}{4}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-360}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -360x \color{red}{-135} & = & \color{red}{252x} +8 \\\Leftrightarrow & -360x \color{red}{-135} \color{blue}{+135} \color{blue}{-252x} & = & \color{red}{252x} +8 \color{blue}{-252x} \color{blue}{+135} \\\Leftrightarrow & -360x-252x& = & 8+135 \\\Leftrightarrow & \color{red}{-612} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-612} & & \\\Leftrightarrow & x = \frac{-143}{612} & & \\ & V = \left\{ \frac{-143}{612} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{100x} +15 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +15 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & -240x-100x& = & 15+48 \\\Leftrightarrow & \color{red}{-340} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-340} & & \\\Leftrightarrow & x = \frac{-63}{340} & & \\ & V = \left\{ \frac{-63}{340} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{9}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-99} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 330x \color{red}{-99} \color{blue}{+99} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+99} \\\Leftrightarrow & 330x+275x& = & 30+99 \\\Leftrightarrow & \color{red}{605} x& = & 129 \\\Leftrightarrow & x = \frac{129}{605} & & \\ & V = \left\{ \frac{129}{605} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{25}{6}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 6 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{50}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-50} & = & \color{red}{-84x} +21 \\\Leftrightarrow & 120x \color{red}{-50} \color{blue}{+50} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{+50} \\\Leftrightarrow & 120x+84x& = & 21+50 \\\Leftrightarrow & \color{red}{204} x& = & 71 \\\Leftrightarrow & x = \frac{71}{204} & & \\ & V = \left\{ \frac{71}{204} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{8}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+88} & = & \color{red}{693x} +54 \\\Leftrightarrow & 990x \color{red}{+88} \color{blue}{-88} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{-88} \\\Leftrightarrow & 990x-693x& = & 54-88 \\\Leftrightarrow & \color{red}{297} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{297} & & \\ & V = \left\{ \frac{-34}{297} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+18} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 252x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & 252x+105x& = & 14-18 \\\Leftrightarrow & \color{red}{357} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{357} & & \\ & V = \left\{ \frac{-4}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & 5x+\frac{7}{6} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-120}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{150x} +35 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-150x} & = & \color{red}{150x} +35 \color{blue}{-150x} \color{blue}{-24} \\\Leftrightarrow & -120x-150x& = & 35-24 \\\Leftrightarrow & \color{red}{-270} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-270} & & \\\Leftrightarrow & x = \frac{-11}{270} & & \\ & V = \left\{ \frac{-11}{270} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{9})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{25}{9}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{275}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-275} & = & \color{red}{693x} +72 \\\Leftrightarrow & 990x \color{red}{-275} \color{blue}{+275} \color{blue}{-693x} & = & \color{red}{693x} +72 \color{blue}{-693x} \color{blue}{+275} \\\Leftrightarrow & 990x-693x& = & 72+275 \\\Leftrightarrow & \color{red}{297} x& = & 347 \\\Leftrightarrow & x = \frac{347}{297} & & \\ & V = \left\{ \frac{347}{297} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{4}{11})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -14x-\frac{28}{11}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x- \frac{252}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{-252} & = & \color{red}{-297x} +110 \\\Leftrightarrow & -1386x \color{red}{-252} \color{blue}{+252} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{+252} \\\Leftrightarrow & -1386x+297x& = & 110+252 \\\Leftrightarrow & \color{red}{-1089} x& = & 362 \\\Leftrightarrow & x = \frac{362}{-1089} & & \\\Leftrightarrow & x = \frac{-362}{1089} & & \\ & V = \left\{ \frac{-362}{1089} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{20}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1125}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1125x \color{red}{+100} & = & \color{red}{135x} +54 \\\Leftrightarrow & 1125x \color{red}{+100} \color{blue}{-100} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{-100} \\\Leftrightarrow & 1125x-135x& = & 54-100 \\\Leftrightarrow & \color{red}{990} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{990} & & \\\Leftrightarrow & x = \frac{-23}{495} & & \\ & V = \left\{ \frac{-23}{495} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-132} & = & \color{red}{275x} +45 \\\Leftrightarrow & 1320x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +45 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 1320x-275x& = & 45+132 \\\Leftrightarrow & \color{red}{1045} x& = & 177 \\\Leftrightarrow & x = \frac{177}{1045} & & \\ & V = \left\{ \frac{177}{1045} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{99x} +88 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{+30} \\\Leftrightarrow & 330x-99x& = & 88+30 \\\Leftrightarrow & \color{red}{231} x& = & 118 \\\Leftrightarrow & x = \frac{118}{231} & & \\ & V = \left\{ \frac{118}{231} \right\} & \\\end{align}\)