Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{9})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{-40} & = & \color{red}{-405x} +54 \\\Leftrightarrow & -360x \color{red}{-40} \color{blue}{+40} \color{blue}{+405x} & = & \color{red}{-405x} +54 \color{blue}{+405x} \color{blue}{+40} \\\Leftrightarrow & -360x+405x& = & 54+40 \\\Leftrightarrow & \color{red}{45} x& = & 94 \\\Leftrightarrow & x = \frac{94}{45} & & \\ & V = \left\{ \frac{94}{45} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 12x+\frac{16}{3}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+80} & = & \color{red}{75x} +6 \\\Leftrightarrow & 180x \color{red}{+80} \color{blue}{-80} \color{blue}{-75x} & = & \color{red}{75x} +6 \color{blue}{-75x} \color{blue}{-80} \\\Leftrightarrow & 180x-75x& = & 6-80 \\\Leftrightarrow & \color{red}{105} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{105} & & \\ & V = \left\{ \frac{-74}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{10})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 6x-\frac{9}{10}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x- \frac{81}{ \color{blue}{90} })& = & (\frac{450}{ \color{blue}{90} }x+ \frac{50}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{-81} & = & \color{red}{450x} +50 \\\Leftrightarrow & 540x \color{red}{-81} \color{blue}{+81} \color{blue}{-450x} & = & \color{red}{450x} +50 \color{blue}{-450x} \color{blue}{+81} \\\Leftrightarrow & 540x-450x& = & 50+81 \\\Leftrightarrow & \color{red}{90} x& = & 131 \\\Leftrightarrow & x = \frac{131}{90} & & \\ & V = \left\{ \frac{131}{90} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{9})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 10x-\frac{4}{9}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{360}{ \color{blue}{36} }x- \frac{16}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 360x \color{red}{-16} & = & \color{red}{252x} +81 \\\Leftrightarrow & 360x \color{red}{-16} \color{blue}{+16} \color{blue}{-252x} & = & \color{red}{252x} +81 \color{blue}{-252x} \color{blue}{+16} \\\Leftrightarrow & 360x-252x& = & 81+16 \\\Leftrightarrow & \color{red}{108} x& = & 97 \\\Leftrightarrow & x = \frac{97}{108} & & \\ & V = \left\{ \frac{97}{108} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{5})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -28x+\frac{21}{5}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x+ \frac{231}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{+231} & = & \color{red}{-495x} +10 \\\Leftrightarrow & -1540x \color{red}{+231} \color{blue}{-231} \color{blue}{+495x} & = & \color{red}{-495x} +10 \color{blue}{+495x} \color{blue}{-231} \\\Leftrightarrow & -1540x+495x& = & 10-231 \\\Leftrightarrow & \color{red}{-1045} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{-1045} & & \\\Leftrightarrow & x = \frac{221}{1045} & & \\ & V = \left\{ \frac{221}{1045} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{1}{3})& = & -8x+\frac{5}{11} \\\Leftrightarrow & -21x+\frac{7}{3}& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+77} & = & \color{red}{-264x} +15 \\\Leftrightarrow & -693x \color{red}{+77} \color{blue}{-77} \color{blue}{+264x} & = & \color{red}{-264x} +15 \color{blue}{+264x} \color{blue}{-77} \\\Leftrightarrow & -693x+264x& = & 15-77 \\\Leftrightarrow & \color{red}{-429} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-429} & & \\\Leftrightarrow & x = \frac{62}{429} & & \\ & V = \left\{ \frac{62}{429} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -2x+\frac{5}{9} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -2x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{+90} & = & \color{red}{-126x} +35 \\\Leftrightarrow & 1575x \color{red}{+90} \color{blue}{-90} \color{blue}{+126x} & = & \color{red}{-126x} +35 \color{blue}{+126x} \color{blue}{-90} \\\Leftrightarrow & 1575x+126x& = & 35-90 \\\Leftrightarrow & \color{red}{1701} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{1701} & & \\ & V = \left\{ \frac{-55}{1701} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{10}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+30} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 315x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & 315x+147x& = & 70-30 \\\Leftrightarrow & \color{red}{462} x& = & 40 \\\Leftrightarrow & x = \frac{40}{462} & & \\\Leftrightarrow & x = \frac{20}{231} & & \\ & V = \left\{ \frac{20}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{11})& = & 8x+\frac{7}{8} \\\Leftrightarrow & -28x+\frac{35}{11}& = & 8x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x+ \frac{280}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{+280} & = & \color{red}{704x} +77 \\\Leftrightarrow & -2464x \color{red}{+280} \color{blue}{-280} \color{blue}{-704x} & = & \color{red}{704x} +77 \color{blue}{-704x} \color{blue}{-280} \\\Leftrightarrow & -2464x-704x& = & 77-280 \\\Leftrightarrow & \color{red}{-3168} x& = & -203 \\\Leftrightarrow & x = \frac{-203}{-3168} & & \\\Leftrightarrow & x = \frac{203}{3168} & & \\ & V = \left\{ \frac{203}{3168} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -24x-\frac{24}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x- \frac{24}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{-24} & = & \color{red}{35x} +10 \\\Leftrightarrow & -168x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & -168x-35x& = & 10+24 \\\Leftrightarrow & \color{red}{-203} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-203} & & \\\Leftrightarrow & x = \frac{-34}{203} & & \\ & V = \left\{ \frac{-34}{203} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{8})& = & 4x+\frac{10}{3} \\\Leftrightarrow & 25x-\frac{25}{8}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x- \frac{75}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{-75} & = & \color{red}{96x} +80 \\\Leftrightarrow & 600x \color{red}{-75} \color{blue}{+75} \color{blue}{-96x} & = & \color{red}{96x} +80 \color{blue}{-96x} \color{blue}{+75} \\\Leftrightarrow & 600x-96x& = & 80+75 \\\Leftrightarrow & \color{red}{504} x& = & 155 \\\Leftrightarrow & x = \frac{155}{504} & & \\ & V = \left\{ \frac{155}{504} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{6}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{-70x} +15 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{+12} \\\Leftrightarrow & -60x+70x& = & 15+12 \\\Leftrightarrow & \color{red}{10} x& = & 27 \\\Leftrightarrow & x = \frac{27}{10} & & \\ & V = \left\{ \frac{27}{10} \right\} & \\\end{align}\)