Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & -9x+\frac{9}{10} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{140}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-140} & = & \color{red}{-270x} +27 \\\Leftrightarrow & 420x \color{red}{-140} \color{blue}{+140} \color{blue}{+270x} & = & \color{red}{-270x} +27 \color{blue}{+270x} \color{blue}{+140} \\\Leftrightarrow & 420x+270x& = & 27+140 \\\Leftrightarrow & \color{red}{690} x& = & 167 \\\Leftrightarrow & x = \frac{167}{690} & & \\ & V = \left\{ \frac{167}{690} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{10})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -21x+\frac{21}{10}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x+ \frac{63}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{40}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{+63} & = & \color{red}{240x} +40 \\\Leftrightarrow & -630x \color{red}{+63} \color{blue}{-63} \color{blue}{-240x} & = & \color{red}{240x} +40 \color{blue}{-240x} \color{blue}{-63} \\\Leftrightarrow & -630x-240x& = & 40-63 \\\Leftrightarrow & \color{red}{-870} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-870} & & \\\Leftrightarrow & x = \frac{23}{870} & & \\ & V = \left\{ \frac{23}{870} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -4x+\frac{6}{5} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+30} & = & \color{red}{-140x} +42 \\\Leftrightarrow & 315x \color{red}{+30} \color{blue}{-30} \color{blue}{+140x} & = & \color{red}{-140x} +42 \color{blue}{+140x} \color{blue}{-30} \\\Leftrightarrow & 315x+140x& = & 42-30 \\\Leftrightarrow & \color{red}{455} x& = & 12 \\\Leftrightarrow & x = \frac{12}{455} & & \\ & V = \left\{ \frac{12}{455} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{5})& = & -4x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{28}{5}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{-84} & = & \color{red}{-60x} +10 \\\Leftrightarrow & 525x \color{red}{-84} \color{blue}{+84} \color{blue}{+60x} & = & \color{red}{-60x} +10 \color{blue}{+60x} \color{blue}{+84} \\\Leftrightarrow & 525x+60x& = & 10+84 \\\Leftrightarrow & \color{red}{585} x& = & 94 \\\Leftrightarrow & x = \frac{94}{585} & & \\ & V = \left\{ \frac{94}{585} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{7})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{112}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 112x \color{red}{+24} & = & \color{red}{196x} +49 \\\Leftrightarrow & 112x \color{red}{+24} \color{blue}{-24} \color{blue}{-196x} & = & \color{red}{196x} +49 \color{blue}{-196x} \color{blue}{-24} \\\Leftrightarrow & 112x-196x& = & 49-24 \\\Leftrightarrow & \color{red}{-84} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-84} & & \\\Leftrightarrow & x = \frac{-25}{84} & & \\ & V = \left\{ \frac{-25}{84} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{8})& = & -9x+\frac{6}{7} \\\Leftrightarrow & -28x+\frac{35}{8}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1568}{ \color{blue}{56} }x+ \frac{245}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1568x \color{red}{+245} & = & \color{red}{-504x} +48 \\\Leftrightarrow & -1568x \color{red}{+245} \color{blue}{-245} \color{blue}{+504x} & = & \color{red}{-504x} +48 \color{blue}{+504x} \color{blue}{-245} \\\Leftrightarrow & -1568x+504x& = & 48-245 \\\Leftrightarrow & \color{red}{-1064} x& = & -197 \\\Leftrightarrow & x = \frac{-197}{-1064} & & \\\Leftrightarrow & x = \frac{197}{1064} & & \\ & V = \left\{ \frac{197}{1064} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 15x-\frac{9}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-99} & = & \color{red}{385x} +20 \\\Leftrightarrow & 825x \color{red}{-99} \color{blue}{+99} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{+99} \\\Leftrightarrow & 825x-385x& = & 20+99 \\\Leftrightarrow & \color{red}{440} x& = & 119 \\\Leftrightarrow & x = \frac{119}{440} & & \\ & V = \left\{ \frac{119}{440} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{75x} +10 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 180x-75x& = & 10+36 \\\Leftrightarrow & \color{red}{105} x& = & 46 \\\Leftrightarrow & x = \frac{46}{105} & & \\ & V = \left\{ \frac{46}{105} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & 4x+\frac{7}{8} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 4x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{32}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{-30} & = & \color{red}{32x} +7 \\\Leftrightarrow & -120x \color{red}{-30} \color{blue}{+30} \color{blue}{-32x} & = & \color{red}{32x} +7 \color{blue}{-32x} \color{blue}{+30} \\\Leftrightarrow & -120x-32x& = & 7+30 \\\Leftrightarrow & \color{red}{-152} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-152} & & \\\Leftrightarrow & x = \frac{-37}{152} & & \\ & V = \left\{ \frac{-37}{152} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{9})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{14}{9}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{-14} & = & \color{red}{18x} +6 \\\Leftrightarrow & 315x \color{red}{-14} \color{blue}{+14} \color{blue}{-18x} & = & \color{red}{18x} +6 \color{blue}{-18x} \color{blue}{+14} \\\Leftrightarrow & 315x-18x& = & 6+14 \\\Leftrightarrow & \color{red}{297} x& = & 20 \\\Leftrightarrow & x = \frac{20}{297} & & \\ & V = \left\{ \frac{20}{297} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & -5x+\frac{7}{4} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{672}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 672x \color{red}{+120} & = & \color{red}{-140x} +49 \\\Leftrightarrow & 672x \color{red}{+120} \color{blue}{-120} \color{blue}{+140x} & = & \color{red}{-140x} +49 \color{blue}{+140x} \color{blue}{-120} \\\Leftrightarrow & 672x+140x& = & 49-120 \\\Leftrightarrow & \color{red}{812} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{812} & & \\ & V = \left\{ \frac{-71}{812} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{5})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x+\frac{6}{5}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+66} & = & \color{red}{385x} +25 \\\Leftrightarrow & -550x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +25 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & -550x-385x& = & 25-66 \\\Leftrightarrow & \color{red}{-935} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-935} & & \\\Leftrightarrow & x = \frac{41}{935} & & \\ & V = \left\{ \frac{41}{935} \right\} & \\\end{align}\)