Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +8 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +8 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 8-12 \\\Leftrightarrow & \color{red}{-85} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-85} & & \\\Leftrightarrow & x = \frac{4}{85} & & \\ & V = \left\{ \frac{4}{85} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 880x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 880x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{1265} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1265} & & \\ & V = \left\{ \frac{162}{1265} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{5})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -35x+\frac{14}{5}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x+ \frac{84}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{+84} & = & \color{red}{-270x} +25 \\\Leftrightarrow & -1050x \color{red}{+84} \color{blue}{-84} \color{blue}{+270x} & = & \color{red}{-270x} +25 \color{blue}{+270x} \color{blue}{-84} \\\Leftrightarrow & -1050x+270x& = & 25-84 \\\Leftrightarrow & \color{red}{-780} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-780} & & \\\Leftrightarrow & x = \frac{59}{780} & & \\ & V = \left\{ \frac{59}{780} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+132} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 330x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 330x+275x& = & 20-132 \\\Leftrightarrow & \color{red}{605} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{605} & & \\ & V = \left\{ \frac{-112}{605} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{4}{7})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 35x-4& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{12}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-12} & = & \color{red}{-6x} +10 \\\Leftrightarrow & 105x \color{red}{-12} \color{blue}{+12} \color{blue}{+6x} & = & \color{red}{-6x} +10 \color{blue}{+6x} \color{blue}{+12} \\\Leftrightarrow & 105x+6x& = & 10+12 \\\Leftrightarrow & \color{red}{111} x& = & 22 \\\Leftrightarrow & x = \frac{22}{111} & & \\ & V = \left\{ \frac{22}{111} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 4x-\frac{6}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{-12} & = & \color{red}{70x} +45 \\\Leftrightarrow & 40x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & 40x-70x& = & 45+12 \\\Leftrightarrow & \color{red}{-30} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-30} & & \\\Leftrightarrow & x = \frac{-19}{10} & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{3})& = & -9x+\frac{3}{10} \\\Leftrightarrow & 10x-\frac{20}{3}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{-200} & = & \color{red}{-270x} +9 \\\Leftrightarrow & 300x \color{red}{-200} \color{blue}{+200} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{+200} \\\Leftrightarrow & 300x+270x& = & 9+200 \\\Leftrightarrow & \color{red}{570} x& = & 209 \\\Leftrightarrow & x = \frac{209}{570} & & \\\Leftrightarrow & x = \frac{11}{30} & & \\ & V = \left\{ \frac{11}{30} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{11})& = & -3x+\frac{5}{6} \\\Leftrightarrow & 4x-\frac{8}{11}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{264}{ \color{blue}{66} }x- \frac{48}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 264x \color{red}{-48} & = & \color{red}{-198x} +55 \\\Leftrightarrow & 264x \color{red}{-48} \color{blue}{+48} \color{blue}{+198x} & = & \color{red}{-198x} +55 \color{blue}{+198x} \color{blue}{+48} \\\Leftrightarrow & 264x+198x& = & 55+48 \\\Leftrightarrow & \color{red}{462} x& = & 103 \\\Leftrightarrow & x = \frac{103}{462} & & \\ & V = \left\{ \frac{103}{462} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -4x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -4x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-30} & = & \color{red}{-140x} +28 \\\Leftrightarrow & 525x \color{red}{-30} \color{blue}{+30} \color{blue}{+140x} & = & \color{red}{-140x} +28 \color{blue}{+140x} \color{blue}{+30} \\\Leftrightarrow & 525x+140x& = & 28+30 \\\Leftrightarrow & \color{red}{665} x& = & 58 \\\Leftrightarrow & x = \frac{58}{665} & & \\ & V = \left\{ \frac{58}{665} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 6x-\frac{4}{5}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{-225x} +20 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{+225x} & = & \color{red}{-225x} +20 \color{blue}{+225x} \color{blue}{+36} \\\Leftrightarrow & 270x+225x& = & 20+36 \\\Leftrightarrow & \color{red}{495} x& = & 56 \\\Leftrightarrow & x = \frac{56}{495} & & \\ & V = \left\{ \frac{56}{495} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-50x} +15 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & 120x+50x& = & 15-24 \\\Leftrightarrow & \color{red}{170} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{170} & & \\ & V = \left\{ \frac{-9}{170} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+154} & = & \color{red}{165x} +12 \\\Leftrightarrow & -462x \color{red}{+154} \color{blue}{-154} \color{blue}{-165x} & = & \color{red}{165x} +12 \color{blue}{-165x} \color{blue}{-154} \\\Leftrightarrow & -462x-165x& = & 12-154 \\\Leftrightarrow & \color{red}{-627} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{-627} & & \\\Leftrightarrow & x = \frac{142}{627} & & \\ & V = \left\{ \frac{142}{627} \right\} & \\\end{align}\)