Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & -18x-\frac{12}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-132} & = & \color{red}{-385x} +56 \\\Leftrightarrow & -1386x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -1386x+385x& = & 56+132 \\\Leftrightarrow & \color{red}{-1001} x& = & 188 \\\Leftrightarrow & x = \frac{188}{-1001} & & \\\Leftrightarrow & x = \frac{-188}{1001} & & \\ & V = \left\{ \frac{-188}{1001} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{8})& = & 4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{15}{8}& = & 4x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{32}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{-15} & = & \color{red}{32x} +12 \\\Leftrightarrow & -120x \color{red}{-15} \color{blue}{+15} \color{blue}{-32x} & = & \color{red}{32x} +12 \color{blue}{-32x} \color{blue}{+15} \\\Leftrightarrow & -120x-32x& = & 12+15 \\\Leftrightarrow & \color{red}{-152} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-152} & & \\\Leftrightarrow & x = \frac{-27}{152} & & \\ & V = \left\{ \frac{-27}{152} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & 4x+\frac{2}{9} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-540}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -540x \color{red}{-135} & = & \color{red}{144x} +8 \\\Leftrightarrow & -540x \color{red}{-135} \color{blue}{+135} \color{blue}{-144x} & = & \color{red}{144x} +8 \color{blue}{-144x} \color{blue}{+135} \\\Leftrightarrow & -540x-144x& = & 8+135 \\\Leftrightarrow & \color{red}{-684} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-684} & & \\\Leftrightarrow & x = \frac{-143}{684} & & \\ & V = \left\{ \frac{-143}{684} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{11})& = & 9x+\frac{6}{7} \\\Leftrightarrow & -18x-\frac{30}{11}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-210} & = & \color{red}{693x} +66 \\\Leftrightarrow & -1386x \color{red}{-210} \color{blue}{+210} \color{blue}{-693x} & = & \color{red}{693x} +66 \color{blue}{-693x} \color{blue}{+210} \\\Leftrightarrow & -1386x-693x& = & 66+210 \\\Leftrightarrow & \color{red}{-2079} x& = & 276 \\\Leftrightarrow & x = \frac{276}{-2079} & & \\\Leftrightarrow & x = \frac{-92}{693} & & \\ & V = \left\{ \frac{-92}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{168}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 168x \color{red}{+60} & = & \color{red}{294x} +35 \\\Leftrightarrow & 168x \color{red}{+60} \color{blue}{-60} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-60} \\\Leftrightarrow & 168x-294x& = & 35-60 \\\Leftrightarrow & \color{red}{-126} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-126} & & \\\Leftrightarrow & x = \frac{25}{126} & & \\ & V = \left\{ \frac{25}{126} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{4}{5})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{28}{5}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{-84} & = & \color{red}{30x} +10 \\\Leftrightarrow & 525x \color{red}{-84} \color{blue}{+84} \color{blue}{-30x} & = & \color{red}{30x} +10 \color{blue}{-30x} \color{blue}{+84} \\\Leftrightarrow & 525x-30x& = & 10+84 \\\Leftrightarrow & \color{red}{495} x& = & 94 \\\Leftrightarrow & x = \frac{94}{495} & & \\ & V = \left\{ \frac{94}{495} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & -7x+\frac{3}{8} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1152}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1152x \color{red}{-64} & = & \color{red}{-504x} +27 \\\Leftrightarrow & -1152x \color{red}{-64} \color{blue}{+64} \color{blue}{+504x} & = & \color{red}{-504x} +27 \color{blue}{+504x} \color{blue}{+64} \\\Leftrightarrow & -1152x+504x& = & 27+64 \\\Leftrightarrow & \color{red}{-648} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-648} & & \\\Leftrightarrow & x = \frac{-91}{648} & & \\ & V = \left\{ \frac{-91}{648} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 3x+\frac{7}{11} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 3x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+154} & = & \color{red}{99x} +21 \\\Leftrightarrow & 924x \color{red}{+154} \color{blue}{-154} \color{blue}{-99x} & = & \color{red}{99x} +21 \color{blue}{-99x} \color{blue}{-154} \\\Leftrightarrow & 924x-99x& = & 21-154 \\\Leftrightarrow & \color{red}{825} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{825} & & \\ & V = \left\{ \frac{-133}{825} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -2x+\frac{2}{5} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -2x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{+105} & = & \color{red}{-80x} +16 \\\Leftrightarrow & -1120x \color{red}{+105} \color{blue}{-105} \color{blue}{+80x} & = & \color{red}{-80x} +16 \color{blue}{+80x} \color{blue}{-105} \\\Leftrightarrow & -1120x+80x& = & 16-105 \\\Leftrightarrow & \color{red}{-1040} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-1040} & & \\\Leftrightarrow & x = \frac{89}{1040} & & \\ & V = \left\{ \frac{89}{1040} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{7})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 6x-\frac{12}{7}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-12} & = & \color{red}{35x} +5 \\\Leftrightarrow & 42x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +5 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 42x-35x& = & 5+12 \\\Leftrightarrow & \color{red}{7} x& = & 17 \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{6})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -28x-\frac{35}{6}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-35} & = & \color{red}{30x} +5 \\\Leftrightarrow & -168x \color{red}{-35} \color{blue}{+35} \color{blue}{-30x} & = & \color{red}{30x} +5 \color{blue}{-30x} \color{blue}{+35} \\\Leftrightarrow & -168x-30x& = & 5+35 \\\Leftrightarrow & \color{red}{-198} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-198} & & \\\Leftrightarrow & x = \frac{-20}{99} & & \\ & V = \left\{ \frac{-20}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{7})& = & 3x+\frac{5}{4} \\\Leftrightarrow & -20x-\frac{20}{7}& = & 3x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-80} & = & \color{red}{84x} +35 \\\Leftrightarrow & -560x \color{red}{-80} \color{blue}{+80} \color{blue}{-84x} & = & \color{red}{84x} +35 \color{blue}{-84x} \color{blue}{+80} \\\Leftrightarrow & -560x-84x& = & 35+80 \\\Leftrightarrow & \color{red}{-644} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-644} & & \\\Leftrightarrow & x = \frac{-5}{28} & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)