Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{-100x} +35 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{+100x} & = & \color{red}{-100x} +35 \color{blue}{+100x} \color{blue}{-48} \\\Leftrightarrow & -240x+100x& = & 35-48 \\\Leftrightarrow & \color{red}{-140} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-140} & & \\\Leftrightarrow & x = \frac{13}{140} & & \\ & V = \left\{ \frac{13}{140} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{49x} +10 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -70x-49x& = & 10+10 \\\Leftrightarrow & \color{red}{-119} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-119} & & \\\Leftrightarrow & x = \frac{-20}{119} & & \\ & V = \left\{ \frac{-20}{119} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{-96} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 240x \color{red}{-96} \color{blue}{+96} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+96} \\\Leftrightarrow & 240x+280x& = & 35+96 \\\Leftrightarrow & \color{red}{520} x& = & 131 \\\Leftrightarrow & x = \frac{131}{520} & & \\ & V = \left\{ \frac{131}{520} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{1}{2})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 14x+\frac{7}{2}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+28} & = & \color{red}{40x} +9 \\\Leftrightarrow & 112x \color{red}{+28} \color{blue}{-28} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{-28} \\\Leftrightarrow & 112x-40x& = & 9-28 \\\Leftrightarrow & \color{red}{72} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{72} & & \\ & V = \left\{ \frac{-19}{72} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-336}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -336x \color{red}{+48} & = & \color{red}{-392x} +49 \\\Leftrightarrow & -336x \color{red}{+48} \color{blue}{-48} \color{blue}{+392x} & = & \color{red}{-392x} +49 \color{blue}{+392x} \color{blue}{-48} \\\Leftrightarrow & -336x+392x& = & 49-48 \\\Leftrightarrow & \color{red}{56} x& = & 1 \\\Leftrightarrow & x = \frac{1}{56} & & \\ & V = \left\{ \frac{1}{56} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{12}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+108} & = & \color{red}{315x} +56 \\\Leftrightarrow & -756x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & -756x-315x& = & 56-108 \\\Leftrightarrow & \color{red}{-1071} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-1071} & & \\\Leftrightarrow & x = \frac{52}{1071} & & \\ & V = \left\{ \frac{52}{1071} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+264} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 660x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & 660x+275x& = & 20-264 \\\Leftrightarrow & \color{red}{935} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{935} & & \\ & V = \left\{ \frac{-244}{935} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{6})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 14x-\frac{35}{6}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-35} & = & \color{red}{18x} +4 \\\Leftrightarrow & 84x \color{red}{-35} \color{blue}{+35} \color{blue}{-18x} & = & \color{red}{18x} +4 \color{blue}{-18x} \color{blue}{+35} \\\Leftrightarrow & 84x-18x& = & 4+35 \\\Leftrightarrow & \color{red}{66} x& = & 39 \\\Leftrightarrow & x = \frac{39}{66} & & \\\Leftrightarrow & x = \frac{13}{22} & & \\ & V = \left\{ \frac{13}{22} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{11})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{30}{11}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-210} & = & \color{red}{385x} +66 \\\Leftrightarrow & 924x \color{red}{-210} \color{blue}{+210} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+210} \\\Leftrightarrow & 924x-385x& = & 66+210 \\\Leftrightarrow & \color{red}{539} x& = & 276 \\\Leftrightarrow & x = \frac{276}{539} & & \\ & V = \left\{ \frac{276}{539} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{11})& = & 3x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{25}{11}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x- \frac{50}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{-50} & = & \color{red}{66x} +33 \\\Leftrightarrow & -440x \color{red}{-50} \color{blue}{+50} \color{blue}{-66x} & = & \color{red}{66x} +33 \color{blue}{-66x} \color{blue}{+50} \\\Leftrightarrow & -440x-66x& = & 33+50 \\\Leftrightarrow & \color{red}{-506} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-506} & & \\\Leftrightarrow & x = \frac{-83}{506} & & \\ & V = \left\{ \frac{-83}{506} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-110} & = & \color{red}{-539x} +14 \\\Leftrightarrow & 462x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & 462x+539x& = & 14+110 \\\Leftrightarrow & \color{red}{1001} x& = & 124 \\\Leftrightarrow & x = \frac{124}{1001} & & \\ & V = \left\{ \frac{124}{1001} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{-135x} +50 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{-12} \\\Leftrightarrow & -60x+135x& = & 50-12 \\\Leftrightarrow & \color{red}{75} x& = & 38 \\\Leftrightarrow & x = \frac{38}{75} & & \\ & V = \left\{ \frac{38}{75} \right\} & \\\end{align}\)