Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{8})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 10x-\frac{25}{8}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x- \frac{175}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{-175} & = & \color{red}{392x} +48 \\\Leftrightarrow & 560x \color{red}{-175} \color{blue}{+175} \color{blue}{-392x} & = & \color{red}{392x} +48 \color{blue}{-392x} \color{blue}{+175} \\\Leftrightarrow & 560x-392x& = & 48+175 \\\Leftrightarrow & \color{red}{168} x& = & 223 \\\Leftrightarrow & x = \frac{223}{168} & & \\ & V = \left\{ \frac{223}{168} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{8}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{+8} & = & \color{red}{27x} +10 \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & -12x-27x& = & 10-8 \\\Leftrightarrow & \color{red}{-39} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-39} & & \\\Leftrightarrow & x = \frac{-2}{39} & & \\ & V = \left\{ \frac{-2}{39} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -2x+\frac{7}{8} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{360}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 360x \color{red}{-96} & = & \color{red}{-80x} +35 \\\Leftrightarrow & 360x \color{red}{-96} \color{blue}{+96} \color{blue}{+80x} & = & \color{red}{-80x} +35 \color{blue}{+80x} \color{blue}{+96} \\\Leftrightarrow & 360x+80x& = & 35+96 \\\Leftrightarrow & \color{red}{440} x& = & 131 \\\Leftrightarrow & x = \frac{131}{440} & & \\ & V = \left\{ \frac{131}{440} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-90} & = & \color{red}{275x} +22 \\\Leftrightarrow & -660x \color{red}{-90} \color{blue}{+90} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{+90} \\\Leftrightarrow & -660x-275x& = & 22+90 \\\Leftrightarrow & \color{red}{-935} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-935} & & \\\Leftrightarrow & x = \frac{-112}{935} & & \\ & V = \left\{ \frac{-112}{935} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 25x-\frac{10}{11}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{-30} & = & \color{red}{297x} +44 \\\Leftrightarrow & 825x \color{red}{-30} \color{blue}{+30} \color{blue}{-297x} & = & \color{red}{297x} +44 \color{blue}{-297x} \color{blue}{+30} \\\Leftrightarrow & 825x-297x& = & 44+30 \\\Leftrightarrow & \color{red}{528} x& = & 74 \\\Leftrightarrow & x = \frac{74}{528} & & \\\Leftrightarrow & x = \frac{37}{264} & & \\ & V = \left\{ \frac{37}{264} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & 630x+147x& = & 70+90 \\\Leftrightarrow & \color{red}{777} x& = & 160 \\\Leftrightarrow & x = \frac{160}{777} & & \\ & V = \left\{ \frac{160}{777} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{9})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 28x+\frac{35}{9}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+35} & = & \color{red}{45x} +8 \\\Leftrightarrow & 252x \color{red}{+35} \color{blue}{-35} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-35} \\\Leftrightarrow & 252x-45x& = & 8-35 \\\Leftrightarrow & \color{red}{207} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{207} & & \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{11})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 18x+\frac{30}{11}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2376}{ \color{blue}{132} }x+ \frac{360}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2376x \color{red}{+360} & = & \color{red}{660x} +55 \\\Leftrightarrow & 2376x \color{red}{+360} \color{blue}{-360} \color{blue}{-660x} & = & \color{red}{660x} +55 \color{blue}{-660x} \color{blue}{-360} \\\Leftrightarrow & 2376x-660x& = & 55-360 \\\Leftrightarrow & \color{red}{1716} x& = & -305 \\\Leftrightarrow & x = \frac{-305}{1716} & & \\ & V = \left\{ \frac{-305}{1716} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-640}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -640x \color{red}{+96} & = & \color{red}{-280x} +45 \\\Leftrightarrow & -640x \color{red}{+96} \color{blue}{-96} \color{blue}{+280x} & = & \color{red}{-280x} +45 \color{blue}{+280x} \color{blue}{-96} \\\Leftrightarrow & -640x+280x& = & 45-96 \\\Leftrightarrow & \color{red}{-360} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-360} & & \\\Leftrightarrow & x = \frac{17}{120} & & \\ & V = \left\{ \frac{17}{120} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -4x-\frac{4}{3}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{-4} & = & \color{red}{15x} +10 \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{-15x} & = & \color{red}{15x} +10 \color{blue}{-15x} \color{blue}{+4} \\\Leftrightarrow & -12x-15x& = & 10+4 \\\Leftrightarrow & \color{red}{-27} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-27} & & \\\Leftrightarrow & x = \frac{-14}{27} & & \\ & V = \left\{ \frac{-14}{27} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -16x-\frac{16}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-112} & = & \color{red}{-147x} +30 \\\Leftrightarrow & -336x \color{red}{-112} \color{blue}{+112} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{+112} \\\Leftrightarrow & -336x+147x& = & 30+112 \\\Leftrightarrow & \color{red}{-189} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-189} & & \\\Leftrightarrow & x = \frac{-142}{189} & & \\ & V = \left\{ \frac{-142}{189} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{3})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -10x+\frac{8}{3}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & -90x+63x& = & 2-24 \\\Leftrightarrow & \color{red}{-27} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-27} & & \\\Leftrightarrow & x = \frac{22}{27} & & \\ & V = \left\{ \frac{22}{27} \right\} & \\\end{align}\)