Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{8})& = & 3x+\frac{8}{7} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-784}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -784x \color{red}{-147} & = & \color{red}{168x} +64 \\\Leftrightarrow & -784x \color{red}{-147} \color{blue}{+147} \color{blue}{-168x} & = & \color{red}{168x} +64 \color{blue}{-168x} \color{blue}{+147} \\\Leftrightarrow & -784x-168x& = & 64+147 \\\Leftrightarrow & \color{red}{-952} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-952} & & \\\Leftrightarrow & x = \frac{-211}{952} & & \\ & V = \left\{ \frac{-211}{952} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{2})& = & 4x+\frac{7}{9} \\\Leftrightarrow & -15x+\frac{25}{2}& = & 4x+\frac{7}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-270}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{72}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -270x \color{red}{+225} & = & \color{red}{72x} +14 \\\Leftrightarrow & -270x \color{red}{+225} \color{blue}{-225} \color{blue}{-72x} & = & \color{red}{72x} +14 \color{blue}{-72x} \color{blue}{-225} \\\Leftrightarrow & -270x-72x& = & 14-225 \\\Leftrightarrow & \color{red}{-342} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{-342} & & \\\Leftrightarrow & x = \frac{211}{342} & & \\ & V = \left\{ \frac{211}{342} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & 120x-50x& = & 45-24 \\\Leftrightarrow & \color{red}{70} x& = & 21 \\\Leftrightarrow & x = \frac{21}{70} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -2x+\frac{2}{9} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-72}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{-135} & = & \color{red}{-72x} +8 \\\Leftrightarrow & 540x \color{red}{-135} \color{blue}{+135} \color{blue}{+72x} & = & \color{red}{-72x} +8 \color{blue}{+72x} \color{blue}{+135} \\\Leftrightarrow & 540x+72x& = & 8+135 \\\Leftrightarrow & \color{red}{612} x& = & 143 \\\Leftrightarrow & x = \frac{143}{612} & & \\ & V = \left\{ \frac{143}{612} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-50} & = & \color{red}{105x} +28 \\\Leftrightarrow & 280x \color{red}{-50} \color{blue}{+50} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{+50} \\\Leftrightarrow & 280x-105x& = & 28+50 \\\Leftrightarrow & \color{red}{175} x& = & 78 \\\Leftrightarrow & x = \frac{78}{175} & & \\ & V = \left\{ \frac{78}{175} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{11})& = & 9x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{10}{11}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+20} & = & \color{red}{198x} +99 \\\Leftrightarrow & 176x \color{red}{+20} \color{blue}{-20} \color{blue}{-198x} & = & \color{red}{198x} +99 \color{blue}{-198x} \color{blue}{-20} \\\Leftrightarrow & 176x-198x& = & 99-20 \\\Leftrightarrow & \color{red}{-22} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-22} & & \\\Leftrightarrow & x = \frac{-79}{22} & & \\ & V = \left\{ \frac{-79}{22} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{11})& = & -8x+\frac{10}{11} \\\Leftrightarrow & -21x+\frac{14}{11}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{14}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+14} & = & \color{red}{-88x} +10 \\\Leftrightarrow & -231x \color{red}{+14} \color{blue}{-14} \color{blue}{+88x} & = & \color{red}{-88x} +10 \color{blue}{+88x} \color{blue}{-14} \\\Leftrightarrow & -231x+88x& = & 10-14 \\\Leftrightarrow & \color{red}{-143} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-143} & & \\\Leftrightarrow & x = \frac{4}{143} & & \\ & V = \left\{ \frac{4}{143} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{10})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 6x-\frac{9}{10}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-9} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 60x \color{red}{-9} \color{blue}{+9} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{+9} \\\Leftrightarrow & 60x+70x& = & 35+9 \\\Leftrightarrow & \color{red}{130} x& = & 44 \\\Leftrightarrow & x = \frac{44}{130} & & \\\Leftrightarrow & x = \frac{22}{65} & & \\ & V = \left\{ \frac{22}{65} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -16x+\frac{8}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+56} & = & \color{red}{441x} +90 \\\Leftrightarrow & -1008x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & -1008x-441x& = & 90-56 \\\Leftrightarrow & \color{red}{-1449} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-1449} & & \\\Leftrightarrow & x = \frac{-34}{1449} & & \\ & V = \left\{ \frac{-34}{1449} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -8x+\frac{4}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+28} & = & \color{red}{315x} +40 \\\Leftrightarrow & -280x \color{red}{+28} \color{blue}{-28} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-28} \\\Leftrightarrow & -280x-315x& = & 40-28 \\\Leftrightarrow & \color{red}{-595} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-595} & & \\\Leftrightarrow & x = \frac{-12}{595} & & \\ & V = \left\{ \frac{-12}{595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1260}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1260x \color{red}{-180} & = & \color{red}{-294x} +35 \\\Leftrightarrow & -1260x \color{red}{-180} \color{blue}{+180} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{+180} \\\Leftrightarrow & -1260x+294x& = & 35+180 \\\Leftrightarrow & \color{red}{-966} x& = & 215 \\\Leftrightarrow & x = \frac{215}{-966} & & \\\Leftrightarrow & x = \frac{-215}{966} & & \\ & V = \left\{ \frac{-215}{966} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -24x-\frac{24}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{-24} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -264x \color{red}{-24} \color{blue}{+24} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{+24} \\\Leftrightarrow & -264x+77x& = & 6+24 \\\Leftrightarrow & \color{red}{-187} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-187} & & \\\Leftrightarrow & x = \frac{-30}{187} & & \\ & V = \left\{ \frac{-30}{187} \right\} & \\\end{align}\)