Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{2})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 12x+\frac{15}{2}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{48}{ \color{blue}{4} }x+ \frac{30}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 48x \color{red}{+30} & = & \color{red}{20x} +3 \\\Leftrightarrow & 48x \color{red}{+30} \color{blue}{-30} \color{blue}{-20x} & = & \color{red}{20x} +3 \color{blue}{-20x} \color{blue}{-30} \\\Leftrightarrow & 48x-20x& = & 3-30 \\\Leftrightarrow & \color{red}{28} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{28} & & \\ & V = \left\{ \frac{-27}{28} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{245x} +42 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{+30} \\\Leftrightarrow & -315x-245x& = & 42+30 \\\Leftrightarrow & \color{red}{-560} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-560} & & \\\Leftrightarrow & x = \frac{-9}{70} & & \\ & V = \left\{ \frac{-9}{70} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-220} & = & \color{red}{99x} +18 \\\Leftrightarrow & 660x \color{red}{-220} \color{blue}{+220} \color{blue}{-99x} & = & \color{red}{99x} +18 \color{blue}{-99x} \color{blue}{+220} \\\Leftrightarrow & 660x-99x& = & 18+220 \\\Leftrightarrow & \color{red}{561} x& = & 238 \\\Leftrightarrow & x = \frac{238}{561} & & \\\Leftrightarrow & x = \frac{14}{33} & & \\ & V = \left\{ \frac{14}{33} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & -2x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -2x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{-10} & = & \color{red}{-14x} +8 \\\Leftrightarrow & 105x \color{red}{-10} \color{blue}{+10} \color{blue}{+14x} & = & \color{red}{-14x} +8 \color{blue}{+14x} \color{blue}{+10} \\\Leftrightarrow & 105x+14x& = & 8+10 \\\Leftrightarrow & \color{red}{119} x& = & 18 \\\Leftrightarrow & x = \frac{18}{119} & & \\ & V = \left\{ \frac{18}{119} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{-165x} +10 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{+165x} & = & \color{red}{-165x} +10 \color{blue}{+165x} \color{blue}{-132} \\\Leftrightarrow & 880x+165x& = & 10-132 \\\Leftrightarrow & \color{red}{1045} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{1045} & & \\ & V = \left\{ \frac{-122}{1045} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{7})& = & 9x+\frac{3}{4} \\\Leftrightarrow & 8x+\frac{4}{7}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{+16} & = & \color{red}{252x} +21 \\\Leftrightarrow & 224x \color{red}{+16} \color{blue}{-16} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{-16} \\\Leftrightarrow & 224x-252x& = & 21-16 \\\Leftrightarrow & \color{red}{-28} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-28} & & \\\Leftrightarrow & x = \frac{-5}{28} & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{300x} +35 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & 720x-300x& = & 35-144 \\\Leftrightarrow & \color{red}{420} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{420} & & \\ & V = \left\{ \frac{-109}{420} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-280}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -280x \color{red}{-100} & = & \color{red}{-630x} +21 \\\Leftrightarrow & -280x \color{red}{-100} \color{blue}{+100} \color{blue}{+630x} & = & \color{red}{-630x} +21 \color{blue}{+630x} \color{blue}{+100} \\\Leftrightarrow & -280x+630x& = & 21+100 \\\Leftrightarrow & \color{red}{350} x& = & 121 \\\Leftrightarrow & x = \frac{121}{350} & & \\ & V = \left\{ \frac{121}{350} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & -360x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{-285} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-285} & & \\\Leftrightarrow & x = \frac{-4}{285} & & \\ & V = \left\{ \frac{-4}{285} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{720}{ \color{blue}{40} }x+ \frac{144}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 720x \color{red}{+144} & = & \color{red}{200x} +25 \\\Leftrightarrow & 720x \color{red}{+144} \color{blue}{-144} \color{blue}{-200x} & = & \color{red}{200x} +25 \color{blue}{-200x} \color{blue}{-144} \\\Leftrightarrow & 720x-200x& = & 25-144 \\\Leftrightarrow & \color{red}{520} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{520} & & \\ & V = \left\{ \frac{-119}{520} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{8})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -35x-\frac{35}{8}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{105}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{20}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{-216x} +20 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{+216x} & = & \color{red}{-216x} +20 \color{blue}{+216x} \color{blue}{+105} \\\Leftrightarrow & -840x+216x& = & 20+105 \\\Leftrightarrow & \color{red}{-624} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-624} & & \\\Leftrightarrow & x = \frac{-125}{624} & & \\ & V = \left\{ \frac{-125}{624} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3300}{ \color{blue}{110} }x+ \frac{240}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3300x \color{red}{+240} & = & \color{red}{770x} +99 \\\Leftrightarrow & 3300x \color{red}{+240} \color{blue}{-240} \color{blue}{-770x} & = & \color{red}{770x} +99 \color{blue}{-770x} \color{blue}{-240} \\\Leftrightarrow & 3300x-770x& = & 99-240 \\\Leftrightarrow & \color{red}{2530} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{2530} & & \\ & V = \left\{ \frac{-141}{2530} \right\} & \\\end{align}\)