Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{-150} & = & \color{red}{-175x} +56 \\\Leftrightarrow & 840x \color{red}{-150} \color{blue}{+150} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{+150} \\\Leftrightarrow & 840x+175x& = & 56+150 \\\Leftrightarrow & \color{red}{1015} x& = & 206 \\\Leftrightarrow & x = \frac{206}{1015} & & \\ & V = \left\{ \frac{206}{1015} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -4x+\frac{10}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-440}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -440x \color{red}{+100} & = & \color{red}{-550x} +33 \\\Leftrightarrow & -440x \color{red}{+100} \color{blue}{-100} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{-100} \\\Leftrightarrow & -440x+550x& = & 33-100 \\\Leftrightarrow & \color{red}{110} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{110} & & \\ & V = \left\{ \frac{-67}{110} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-24} & = & \color{red}{70x} +25 \\\Leftrightarrow & -200x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & -200x-70x& = & 25+24 \\\Leftrightarrow & \color{red}{-270} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-270} & & \\\Leftrightarrow & x = \frac{-49}{270} & & \\ & V = \left\{ \frac{-49}{270} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{-275x} +10 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 660x+275x& = & 10-132 \\\Leftrightarrow & \color{red}{935} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{935} & & \\ & V = \left\{ \frac{-122}{935} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3168}{ \color{blue}{132} }x- \frac{216}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3168x \color{red}{-216} & = & \color{red}{-924x} +77 \\\Leftrightarrow & -3168x \color{red}{-216} \color{blue}{+216} \color{blue}{+924x} & = & \color{red}{-924x} +77 \color{blue}{+924x} \color{blue}{+216} \\\Leftrightarrow & -3168x+924x& = & 77+216 \\\Leftrightarrow & \color{red}{-2244} x& = & 293 \\\Leftrightarrow & x = \frac{293}{-2244} & & \\\Leftrightarrow & x = \frac{-293}{2244} & & \\ & V = \left\{ \frac{-293}{2244} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{8})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -12x-\frac{15}{8}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-288}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{28}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -288x \color{red}{-45} & = & \color{red}{-120x} +28 \\\Leftrightarrow & -288x \color{red}{-45} \color{blue}{+45} \color{blue}{+120x} & = & \color{red}{-120x} +28 \color{blue}{+120x} \color{blue}{+45} \\\Leftrightarrow & -288x+120x& = & 28+45 \\\Leftrightarrow & \color{red}{-168} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-168} & & \\\Leftrightarrow & x = \frac{-73}{168} & & \\ & V = \left\{ \frac{-73}{168} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 20x+\frac{8}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{+32} & = & \color{red}{-196x} +21 \\\Leftrightarrow & 560x \color{red}{+32} \color{blue}{-32} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{-32} \\\Leftrightarrow & 560x+196x& = & 21-32 \\\Leftrightarrow & \color{red}{756} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{756} & & \\ & V = \left\{ \frac{-11}{756} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-132} & = & \color{red}{275x} +30 \\\Leftrightarrow & 1320x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 1320x-275x& = & 30+132 \\\Leftrightarrow & \color{red}{1045} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1045} & & \\ & V = \left\{ \frac{162}{1045} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+60} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 168x \color{red}{+60} \color{blue}{-60} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-60} \\\Leftrightarrow & 168x+70x& = & 35-60 \\\Leftrightarrow & \color{red}{238} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{238} & & \\ & V = \left\{ \frac{-25}{238} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{-8} & = & \color{red}{-45x} +7 \\\Leftrightarrow & 54x \color{red}{-8} \color{blue}{+8} \color{blue}{+45x} & = & \color{red}{-45x} +7 \color{blue}{+45x} \color{blue}{+8} \\\Leftrightarrow & 54x+45x& = & 7+8 \\\Leftrightarrow & \color{red}{99} x& = & 15 \\\Leftrightarrow & x = \frac{15}{99} & & \\\Leftrightarrow & x = \frac{5}{33} & & \\ & V = \left\{ \frac{5}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{8})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{15}{8}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+75} & = & \color{red}{200x} +48 \\\Leftrightarrow & 240x \color{red}{+75} \color{blue}{-75} \color{blue}{-200x} & = & \color{red}{200x} +48 \color{blue}{-200x} \color{blue}{-75} \\\Leftrightarrow & 240x-200x& = & 48-75 \\\Leftrightarrow & \color{red}{40} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{40} & & \\ & V = \left\{ \frac{-27}{40} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{16}{3}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+16} & = & \color{red}{-27x} +2 \\\Leftrightarrow & 60x \color{red}{+16} \color{blue}{-16} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{-16} \\\Leftrightarrow & 60x+27x& = & 2-16 \\\Leftrightarrow & \color{red}{87} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{87} & & \\ & V = \left\{ \frac{-14}{87} \right\} & \\\end{align}\)