Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 18x-\frac{12}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-84} & = & \color{red}{539x} +44 \\\Leftrightarrow & 1386x \color{red}{-84} \color{blue}{+84} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{+84} \\\Leftrightarrow & 1386x-539x& = & 44+84 \\\Leftrightarrow & \color{red}{847} x& = & 128 \\\Leftrightarrow & x = \frac{128}{847} & & \\ & V = \left\{ \frac{128}{847} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{4})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 20x-\frac{15}{4}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-135} & = & \color{red}{324x} +8 \\\Leftrightarrow & 720x \color{red}{-135} \color{blue}{+135} \color{blue}{-324x} & = & \color{red}{324x} +8 \color{blue}{-324x} \color{blue}{+135} \\\Leftrightarrow & 720x-324x& = & 8+135 \\\Leftrightarrow & \color{red}{396} x& = & 143 \\\Leftrightarrow & x = \frac{143}{396} & & \\\Leftrightarrow & x = \frac{13}{36} & & \\ & V = \left\{ \frac{13}{36} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-10} & = & \color{red}{49x} +4 \\\Leftrightarrow & -140x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -140x-49x& = & 4+10 \\\Leftrightarrow & \color{red}{-189} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-189} & & \\\Leftrightarrow & x = \frac{-2}{27} & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2640}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2640x \color{red}{-144} & = & \color{red}{-616x} +99 \\\Leftrightarrow & -2640x \color{red}{-144} \color{blue}{+144} \color{blue}{+616x} & = & \color{red}{-616x} +99 \color{blue}{+616x} \color{blue}{+144} \\\Leftrightarrow & -2640x+616x& = & 99+144 \\\Leftrightarrow & \color{red}{-2024} x& = & 243 \\\Leftrightarrow & x = \frac{243}{-2024} & & \\\Leftrightarrow & x = \frac{-243}{2024} & & \\ & V = \left\{ \frac{-243}{2024} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & 8x+\frac{9}{8} \\\Leftrightarrow & -15x-\frac{6}{7}& = & 8x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{448}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-48} & = & \color{red}{448x} +63 \\\Leftrightarrow & -840x \color{red}{-48} \color{blue}{+48} \color{blue}{-448x} & = & \color{red}{448x} +63 \color{blue}{-448x} \color{blue}{+48} \\\Leftrightarrow & -840x-448x& = & 63+48 \\\Leftrightarrow & \color{red}{-1288} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-1288} & & \\\Leftrightarrow & x = \frac{-111}{1288} & & \\ & V = \left\{ \frac{-111}{1288} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{10}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+20} & = & \color{red}{-70x} +21 \\\Leftrightarrow & 112x \color{red}{+20} \color{blue}{-20} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{-20} \\\Leftrightarrow & 112x+70x& = & 21-20 \\\Leftrightarrow & \color{red}{182} x& = & 1 \\\Leftrightarrow & x = \frac{1}{182} & & \\ & V = \left\{ \frac{1}{182} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{3})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+140} & = & \color{red}{147x} +9 \\\Leftrightarrow & 210x \color{red}{+140} \color{blue}{-140} \color{blue}{-147x} & = & \color{red}{147x} +9 \color{blue}{-147x} \color{blue}{-140} \\\Leftrightarrow & 210x-147x& = & 9-140 \\\Leftrightarrow & \color{red}{63} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{63} & & \\ & V = \left\{ \frac{-131}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{2})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -21x+\frac{35}{2}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x+ \frac{105}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{+105} & = & \color{red}{48x} +16 \\\Leftrightarrow & -126x \color{red}{+105} \color{blue}{-105} \color{blue}{-48x} & = & \color{red}{48x} +16 \color{blue}{-48x} \color{blue}{-105} \\\Leftrightarrow & -126x-48x& = & 16-105 \\\Leftrightarrow & \color{red}{-174} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-174} & & \\\Leftrightarrow & x = \frac{89}{174} & & \\ & V = \left\{ \frac{89}{174} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & -3x+\frac{7}{12} \\\Leftrightarrow & 25x+\frac{20}{3}& = & -3x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+80} & = & \color{red}{-36x} +7 \\\Leftrightarrow & 300x \color{red}{+80} \color{blue}{-80} \color{blue}{+36x} & = & \color{red}{-36x} +7 \color{blue}{+36x} \color{blue}{-80} \\\Leftrightarrow & 300x+36x& = & 7-80 \\\Leftrightarrow & \color{red}{336} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{336} & & \\ & V = \left\{ \frac{-73}{336} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & -120x-50x& = & 45+24 \\\Leftrightarrow & \color{red}{-170} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-170} & & \\\Leftrightarrow & x = \frac{-69}{170} & & \\ & V = \left\{ \frac{-69}{170} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{3})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -35x-\frac{28}{3}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-308} & = & \color{red}{297x} +15 \\\Leftrightarrow & -1155x \color{red}{-308} \color{blue}{+308} \color{blue}{-297x} & = & \color{red}{297x} +15 \color{blue}{-297x} \color{blue}{+308} \\\Leftrightarrow & -1155x-297x& = & 15+308 \\\Leftrightarrow & \color{red}{-1452} x& = & 323 \\\Leftrightarrow & x = \frac{323}{-1452} & & \\\Leftrightarrow & x = \frac{-323}{1452} & & \\ & V = \left\{ \frac{-323}{1452} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 8x+\frac{4}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{+24} & = & \color{red}{150x} +25 \\\Leftrightarrow & 240x \color{red}{+24} \color{blue}{-24} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{-24} \\\Leftrightarrow & 240x-150x& = & 25-24 \\\Leftrightarrow & \color{red}{90} x& = & 1 \\\Leftrightarrow & x = \frac{1}{90} & & \\ & V = \left\{ \frac{1}{90} \right\} & \\\end{align}\)