Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+6} & = & \color{red}{35x} +4 \\\Leftrightarrow & 28x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & 28x-35x& = & 4-6 \\\Leftrightarrow & \color{red}{-7} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-7} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 25x-\frac{10}{7}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-10} & = & \color{red}{-14x} +10 \\\Leftrightarrow & 175x \color{red}{-10} \color{blue}{+10} \color{blue}{+14x} & = & \color{red}{-14x} +10 \color{blue}{+14x} \color{blue}{+10} \\\Leftrightarrow & 175x+14x& = & 10+10 \\\Leftrightarrow & \color{red}{189} x& = & 20 \\\Leftrightarrow & x = \frac{20}{189} & & \\ & V = \left\{ \frac{20}{189} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & 8x+\frac{7}{12} \\\Leftrightarrow & -18x-\frac{18}{5}& = & 8x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1080}{ \color{blue}{60} }x- \frac{216}{ \color{blue}{60} })& = & (\frac{480}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1080x \color{red}{-216} & = & \color{red}{480x} +35 \\\Leftrightarrow & -1080x \color{red}{-216} \color{blue}{+216} \color{blue}{-480x} & = & \color{red}{480x} +35 \color{blue}{-480x} \color{blue}{+216} \\\Leftrightarrow & -1080x-480x& = & 35+216 \\\Leftrightarrow & \color{red}{-1560} x& = & 251 \\\Leftrightarrow & x = \frac{251}{-1560} & & \\\Leftrightarrow & x = \frac{-251}{1560} & & \\ & V = \left\{ \frac{-251}{1560} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-50x} +3 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -120x+50x& = & 3-24 \\\Leftrightarrow & \color{red}{-70} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-70} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -9x+\frac{12}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+60} & = & \color{red}{385x} +44 \\\Leftrightarrow & -495x \color{red}{+60} \color{blue}{-60} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-60} \\\Leftrightarrow & -495x-385x& = & 44-60 \\\Leftrightarrow & \color{red}{-880} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-880} & & \\\Leftrightarrow & x = \frac{1}{55} & & \\ & V = \left\{ \frac{1}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-6} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 42x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & 42x+35x& = & 10+6 \\\Leftrightarrow & \color{red}{77} x& = & 16 \\\Leftrightarrow & x = \frac{16}{77} & & \\ & V = \left\{ \frac{16}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{24}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-24} & = & \color{red}{70x} +49 \\\Leftrightarrow & 168x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 168x-70x& = & 49+24 \\\Leftrightarrow & \color{red}{98} x& = & 73 \\\Leftrightarrow & x = \frac{73}{98} & & \\ & V = \left\{ \frac{73}{98} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{-99x} +24 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+99x} & = & \color{red}{-99x} +24 \color{blue}{+99x} \color{blue}{+154} \\\Leftrightarrow & 1155x+99x& = & 24+154 \\\Leftrightarrow & \color{red}{1254} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1254} & & \\\Leftrightarrow & x = \frac{89}{627} & & \\ & V = \left\{ \frac{89}{627} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{4}{9} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2376}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2376x \color{red}{+162} & = & \color{red}{-495x} +44 \\\Leftrightarrow & -2376x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & -2376x+495x& = & 44-162 \\\Leftrightarrow & \color{red}{-1881} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-1881} & & \\\Leftrightarrow & x = \frac{118}{1881} & & \\ & V = \left\{ \frac{118}{1881} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+108} & = & \color{red}{495x} +88 \\\Leftrightarrow & -1188x \color{red}{+108} \color{blue}{-108} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{-108} \\\Leftrightarrow & -1188x-495x& = & 88-108 \\\Leftrightarrow & \color{red}{-1683} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-1683} & & \\\Leftrightarrow & x = \frac{20}{1683} & & \\ & V = \left\{ \frac{20}{1683} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -2x+\frac{5}{8} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{360}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 360x \color{red}{-96} & = & \color{red}{-80x} +25 \\\Leftrightarrow & 360x \color{red}{-96} \color{blue}{+96} \color{blue}{+80x} & = & \color{red}{-80x} +25 \color{blue}{+80x} \color{blue}{+96} \\\Leftrightarrow & 360x+80x& = & 25+96 \\\Leftrightarrow & \color{red}{440} x& = & 121 \\\Leftrightarrow & x = \frac{121}{440} & & \\\Leftrightarrow & x = \frac{11}{40} & & \\ & V = \left\{ \frac{11}{40} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{8})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{840}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 840x \color{red}{+105} & = & \color{red}{-224x} +80 \\\Leftrightarrow & 840x \color{red}{+105} \color{blue}{-105} \color{blue}{+224x} & = & \color{red}{-224x} +80 \color{blue}{+224x} \color{blue}{-105} \\\Leftrightarrow & 840x+224x& = & 80-105 \\\Leftrightarrow & \color{red}{1064} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{1064} & & \\ & V = \left\{ \frac{-25}{1064} \right\} & \\\end{align}\)