Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{3})& = & 6x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{35}{3}& = & 6x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{35}{ \color{blue}{3} })& = & (\frac{18}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-35} & = & \color{red}{18x} +2 \\\Leftrightarrow & 105x \color{red}{-35} \color{blue}{+35} \color{blue}{-18x} & = & \color{red}{18x} +2 \color{blue}{-18x} \color{blue}{+35} \\\Leftrightarrow & 105x-18x& = & 2+35 \\\Leftrightarrow & \color{red}{87} x& = & 37 \\\Leftrightarrow & x = \frac{37}{87} & & \\ & V = \left\{ \frac{37}{87} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{11})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{15}{11}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-45} & = & \color{red}{99x} +110 \\\Leftrightarrow & -660x \color{red}{-45} \color{blue}{+45} \color{blue}{-99x} & = & \color{red}{99x} +110 \color{blue}{-99x} \color{blue}{+45} \\\Leftrightarrow & -660x-99x& = & 110+45 \\\Leftrightarrow & \color{red}{-759} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-759} & & \\\Leftrightarrow & x = \frac{-155}{759} & & \\ & V = \left\{ \frac{-155}{759} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{+48} \\\Leftrightarrow & -240x+100x& = & 45+48 \\\Leftrightarrow & \color{red}{-140} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-140} & & \\\Leftrightarrow & x = \frac{-93}{140} & & \\ & V = \left\{ \frac{-93}{140} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+132} & = & \color{red}{-495x} +50 \\\Leftrightarrow & 440x \color{red}{+132} \color{blue}{-132} \color{blue}{+495x} & = & \color{red}{-495x} +50 \color{blue}{+495x} \color{blue}{-132} \\\Leftrightarrow & 440x+495x& = & 50-132 \\\Leftrightarrow & \color{red}{935} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{935} & & \\ & V = \left\{ \frac{-82}{935} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{7})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 18x+\frac{18}{7}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x+ \frac{162}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{+162} & = & \color{red}{-315x} +35 \\\Leftrightarrow & 1134x \color{red}{+162} \color{blue}{-162} \color{blue}{+315x} & = & \color{red}{-315x} +35 \color{blue}{+315x} \color{blue}{-162} \\\Leftrightarrow & 1134x+315x& = & 35-162 \\\Leftrightarrow & \color{red}{1449} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{1449} & & \\ & V = \left\{ \frac{-127}{1449} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{8}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-24} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 264x \color{red}{-24} \color{blue}{+24} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+24} \\\Leftrightarrow & 264x+165x& = & 88+24 \\\Leftrightarrow & \color{red}{429} x& = & 112 \\\Leftrightarrow & x = \frac{112}{429} & & \\ & V = \left\{ \frac{112}{429} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{9})& = & 6x+\frac{7}{9} \\\Leftrightarrow & -35x-\frac{14}{9}& = & 6x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{54}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-14} & = & \color{red}{54x} +7 \\\Leftrightarrow & -315x \color{red}{-14} \color{blue}{+14} \color{blue}{-54x} & = & \color{red}{54x} +7 \color{blue}{-54x} \color{blue}{+14} \\\Leftrightarrow & -315x-54x& = & 7+14 \\\Leftrightarrow & \color{red}{-369} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-369} & & \\\Leftrightarrow & x = \frac{-7}{123} & & \\ & V = \left\{ \frac{-7}{123} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{11})& = & -5x+\frac{7}{12} \\\Leftrightarrow & -24x+\frac{12}{11}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3168}{ \color{blue}{132} }x+ \frac{144}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3168x \color{red}{+144} & = & \color{red}{-660x} +77 \\\Leftrightarrow & -3168x \color{red}{+144} \color{blue}{-144} \color{blue}{+660x} & = & \color{red}{-660x} +77 \color{blue}{+660x} \color{blue}{-144} \\\Leftrightarrow & -3168x+660x& = & 77-144 \\\Leftrightarrow & \color{red}{-2508} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-2508} & & \\\Leftrightarrow & x = \frac{67}{2508} & & \\ & V = \left\{ \frac{67}{2508} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{9})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -16x+\frac{16}{9}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1152}{ \color{blue}{72} }x+ \frac{128}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1152x \color{red}{+128} & = & \color{red}{504x} +81 \\\Leftrightarrow & -1152x \color{red}{+128} \color{blue}{-128} \color{blue}{-504x} & = & \color{red}{504x} +81 \color{blue}{-504x} \color{blue}{-128} \\\Leftrightarrow & -1152x-504x& = & 81-128 \\\Leftrightarrow & \color{red}{-1656} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-1656} & & \\\Leftrightarrow & x = \frac{47}{1656} & & \\ & V = \left\{ \frac{47}{1656} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-110} & = & \color{red}{539x} +56 \\\Leftrightarrow & 1540x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & 1540x-539x& = & 56+110 \\\Leftrightarrow & \color{red}{1001} x& = & 166 \\\Leftrightarrow & x = \frac{166}{1001} & & \\ & V = \left\{ \frac{166}{1001} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{-49x} +8 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & 168x+49x& = & 8-30 \\\Leftrightarrow & \color{red}{217} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{217} & & \\ & V = \left\{ \frac{-22}{217} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{3})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 15x+\frac{10}{3}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{135}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 135x \color{red}{+30} & = & \color{red}{63x} +5 \\\Leftrightarrow & 135x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & 135x-63x& = & 5-30 \\\Leftrightarrow & \color{red}{72} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{72} & & \\ & V = \left\{ \frac{-25}{72} \right\} & \\\end{align}\)