Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{20}{3}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-96}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{-80} & = & \color{red}{108x} +27 \\\Leftrightarrow & -96x \color{red}{-80} \color{blue}{+80} \color{blue}{-108x} & = & \color{red}{108x} +27 \color{blue}{-108x} \color{blue}{+80} \\\Leftrightarrow & -96x-108x& = & 27+80 \\\Leftrightarrow & \color{red}{-204} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-204} & & \\\Leftrightarrow & x = \frac{-107}{204} & & \\ & V = \left\{ \frac{-107}{204} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{1}{3})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -14x+\frac{7}{3}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{+7} & = & \color{red}{-9x} +2 \\\Leftrightarrow & -42x \color{red}{+7} \color{blue}{-7} \color{blue}{+9x} & = & \color{red}{-9x} +2 \color{blue}{+9x} \color{blue}{-7} \\\Leftrightarrow & -42x+9x& = & 2-7 \\\Leftrightarrow & \color{red}{-33} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-33} & & \\\Leftrightarrow & x = \frac{5}{33} & & \\ & V = \left\{ \frac{5}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{6})& = & -9x+\frac{2}{9} \\\Leftrightarrow & -25x+\frac{25}{6}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x+ \frac{75}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{+75} & = & \color{red}{-162x} +4 \\\Leftrightarrow & -450x \color{red}{+75} \color{blue}{-75} \color{blue}{+162x} & = & \color{red}{-162x} +4 \color{blue}{+162x} \color{blue}{-75} \\\Leftrightarrow & -450x+162x& = & 4-75 \\\Leftrightarrow & \color{red}{-288} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-288} & & \\\Leftrightarrow & x = \frac{71}{288} & & \\ & V = \left\{ \frac{71}{288} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{4})& = & 6x+\frac{2}{7} \\\Leftrightarrow & 25x+\frac{25}{4}& = & 6x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{175}{ \color{blue}{28} })& = & (\frac{168}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+175} & = & \color{red}{168x} +8 \\\Leftrightarrow & 700x \color{red}{+175} \color{blue}{-175} \color{blue}{-168x} & = & \color{red}{168x} +8 \color{blue}{-168x} \color{blue}{-175} \\\Leftrightarrow & 700x-168x& = & 8-175 \\\Leftrightarrow & \color{red}{532} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{532} & & \\ & V = \left\{ \frac{-167}{532} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -9x+\frac{15}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{+15} & = & \color{red}{-55x} +2 \\\Leftrightarrow & -99x \color{red}{+15} \color{blue}{-15} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{-15} \\\Leftrightarrow & -99x+55x& = & 2-15 \\\Leftrightarrow & \color{red}{-44} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-44} & & \\\Leftrightarrow & x = \frac{13}{44} & & \\ & V = \left\{ \frac{13}{44} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+18} & = & \color{red}{63x} +28 \\\Leftrightarrow & 210x \color{red}{+18} \color{blue}{-18} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{-18} \\\Leftrightarrow & 210x-63x& = & 28-18 \\\Leftrightarrow & \color{red}{147} x& = & 10 \\\Leftrightarrow & x = \frac{10}{147} & & \\ & V = \left\{ \frac{10}{147} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-12} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -84x \color{red}{-12} \color{blue}{+12} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+12} \\\Leftrightarrow & -84x+98x& = & 21+12 \\\Leftrightarrow & \color{red}{14} x& = & 33 \\\Leftrightarrow & x = \frac{33}{14} & & \\ & V = \left\{ \frac{33}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{-147x} +56 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & 126x+147x& = & 56+18 \\\Leftrightarrow & \color{red}{273} x& = & 74 \\\Leftrightarrow & x = \frac{74}{273} & & \\ & V = \left\{ \frac{74}{273} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{5})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-18} & = & \color{red}{20x} +45 \\\Leftrightarrow & 90x \color{red}{-18} \color{blue}{+18} \color{blue}{-20x} & = & \color{red}{20x} +45 \color{blue}{-20x} \color{blue}{+18} \\\Leftrightarrow & 90x-20x& = & 45+18 \\\Leftrightarrow & \color{red}{70} x& = & 63 \\\Leftrightarrow & x = \frac{63}{70} & & \\\Leftrightarrow & x = \frac{9}{10} & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{+154} & = & \color{red}{-297x} +12 \\\Leftrightarrow & 924x \color{red}{+154} \color{blue}{-154} \color{blue}{+297x} & = & \color{red}{-297x} +12 \color{blue}{+297x} \color{blue}{-154} \\\Leftrightarrow & 924x+297x& = & 12-154 \\\Leftrightarrow & \color{red}{1221} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{1221} & & \\ & V = \left\{ \frac{-142}{1221} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{3})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 21x-\frac{35}{3}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-70} & = & \color{red}{12x} +5 \\\Leftrightarrow & 126x \color{red}{-70} \color{blue}{+70} \color{blue}{-12x} & = & \color{red}{12x} +5 \color{blue}{-12x} \color{blue}{+70} \\\Leftrightarrow & 126x-12x& = & 5+70 \\\Leftrightarrow & \color{red}{114} x& = & 75 \\\Leftrightarrow & x = \frac{75}{114} & & \\\Leftrightarrow & x = \frac{25}{38} & & \\ & V = \left\{ \frac{25}{38} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{6})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{35}{6}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{+175} & = & \color{red}{-90x} +36 \\\Leftrightarrow & -420x \color{red}{+175} \color{blue}{-175} \color{blue}{+90x} & = & \color{red}{-90x} +36 \color{blue}{+90x} \color{blue}{-175} \\\Leftrightarrow & -420x+90x& = & 36-175 \\\Leftrightarrow & \color{red}{-330} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-330} & & \\\Leftrightarrow & x = \frac{139}{330} & & \\ & V = \left\{ \frac{139}{330} \right\} & \\\end{align}\)