Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{7})& = & -2x+\frac{7}{5} \\\Leftrightarrow & 9x+\frac{15}{7}& = & -2x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+75} & = & \color{red}{-70x} +49 \\\Leftrightarrow & 315x \color{red}{+75} \color{blue}{-75} \color{blue}{+70x} & = & \color{red}{-70x} +49 \color{blue}{+70x} \color{blue}{-75} \\\Leftrightarrow & 315x+70x& = & 49-75 \\\Leftrightarrow & \color{red}{385} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{385} & & \\ & V = \left\{ \frac{-26}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-224}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{-105} & = & \color{red}{-224x} +36 \\\Leftrightarrow & -420x \color{red}{-105} \color{blue}{+105} \color{blue}{+224x} & = & \color{red}{-224x} +36 \color{blue}{+224x} \color{blue}{+105} \\\Leftrightarrow & -420x+224x& = & 36+105 \\\Leftrightarrow & \color{red}{-196} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-196} & & \\\Leftrightarrow & x = \frac{-141}{196} & & \\ & V = \left\{ \frac{-141}{196} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{2})& = & -3x+\frac{7}{11} \\\Leftrightarrow & 20x+\frac{15}{2}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{14}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+165} & = & \color{red}{-66x} +14 \\\Leftrightarrow & 440x \color{red}{+165} \color{blue}{-165} \color{blue}{+66x} & = & \color{red}{-66x} +14 \color{blue}{+66x} \color{blue}{-165} \\\Leftrightarrow & 440x+66x& = & 14-165 \\\Leftrightarrow & \color{red}{506} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{506} & & \\ & V = \left\{ \frac{-151}{506} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{9})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{25}{9}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1080}{ \color{blue}{72} }x- \frac{200}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1080x \color{red}{-200} & = & \color{red}{504x} +63 \\\Leftrightarrow & 1080x \color{red}{-200} \color{blue}{+200} \color{blue}{-504x} & = & \color{red}{504x} +63 \color{blue}{-504x} \color{blue}{+200} \\\Leftrightarrow & 1080x-504x& = & 63+200 \\\Leftrightarrow & \color{red}{576} x& = & 263 \\\Leftrightarrow & x = \frac{263}{576} & & \\ & V = \left\{ \frac{263}{576} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{6}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{99x} +88 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{-18} \\\Leftrightarrow & -264x-99x& = & 88-18 \\\Leftrightarrow & \color{red}{-363} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-363} & & \\\Leftrightarrow & x = \frac{-70}{363} & & \\ & V = \left\{ \frac{-70}{363} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{3})& = & 9x+\frac{5}{11} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+220} & = & \color{red}{297x} +15 \\\Leftrightarrow & 264x \color{red}{+220} \color{blue}{-220} \color{blue}{-297x} & = & \color{red}{297x} +15 \color{blue}{-297x} \color{blue}{-220} \\\Leftrightarrow & 264x-297x& = & 15-220 \\\Leftrightarrow & \color{red}{-33} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-33} & & \\\Leftrightarrow & x = \frac{205}{33} & & \\ & V = \left\{ \frac{205}{33} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 2x+\frac{7}{2} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{-21} & = & \color{red}{16x} +28 \\\Leftrightarrow & 168x \color{red}{-21} \color{blue}{+21} \color{blue}{-16x} & = & \color{red}{16x} +28 \color{blue}{-16x} \color{blue}{+21} \\\Leftrightarrow & 168x-16x& = & 28+21 \\\Leftrightarrow & \color{red}{152} x& = & 49 \\\Leftrightarrow & x = \frac{49}{152} & & \\ & V = \left\{ \frac{49}{152} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+40} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 420x \color{red}{+40} \color{blue}{-40} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-40} \\\Leftrightarrow & 420x+175x& = & 28-40 \\\Leftrightarrow & \color{red}{595} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{595} & & \\ & V = \left\{ \frac{-12}{595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & 7x+\frac{5}{8} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1200}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1200x \color{red}{-192} & = & \color{red}{280x} +25 \\\Leftrightarrow & 1200x \color{red}{-192} \color{blue}{+192} \color{blue}{-280x} & = & \color{red}{280x} +25 \color{blue}{-280x} \color{blue}{+192} \\\Leftrightarrow & 1200x-280x& = & 25+192 \\\Leftrightarrow & \color{red}{920} x& = & 217 \\\Leftrightarrow & x = \frac{217}{920} & & \\ & V = \left\{ \frac{217}{920} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{9})& = & 3x+\frac{3}{10} \\\Leftrightarrow & 10x-\frac{20}{9}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{900}{ \color{blue}{90} }x- \frac{200}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 900x \color{red}{-200} & = & \color{red}{270x} +27 \\\Leftrightarrow & 900x \color{red}{-200} \color{blue}{+200} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+200} \\\Leftrightarrow & 900x-270x& = & 27+200 \\\Leftrightarrow & \color{red}{630} x& = & 227 \\\Leftrightarrow & x = \frac{227}{630} & & \\ & V = \left\{ \frac{227}{630} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{14}{3}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{+14} & = & \color{red}{27x} +4 \\\Leftrightarrow & 42x \color{red}{+14} \color{blue}{-14} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{-14} \\\Leftrightarrow & 42x-27x& = & 4-14 \\\Leftrightarrow & \color{red}{15} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{15} & & \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{10})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{9}{10}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-9} & = & \color{red}{70x} +12 \\\Leftrightarrow & 150x \color{red}{-9} \color{blue}{+9} \color{blue}{-70x} & = & \color{red}{70x} +12 \color{blue}{-70x} \color{blue}{+9} \\\Leftrightarrow & 150x-70x& = & 12+9 \\\Leftrightarrow & \color{red}{80} x& = & 21 \\\Leftrightarrow & x = \frac{21}{80} & & \\ & V = \left\{ \frac{21}{80} \right\} & \\\end{align}\)