Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{12}{11}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-36} & = & \color{red}{-99x} +44 \\\Leftrightarrow & -660x \color{red}{-36} \color{blue}{+36} \color{blue}{+99x} & = & \color{red}{-99x} +44 \color{blue}{+99x} \color{blue}{+36} \\\Leftrightarrow & -660x+99x& = & 44+36 \\\Leftrightarrow & \color{red}{-561} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-561} & & \\\Leftrightarrow & x = \frac{-80}{561} & & \\ & V = \left\{ \frac{-80}{561} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{8})& = & -8x+\frac{3}{8} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -8x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{-15} & = & \color{red}{-64x} +3 \\\Leftrightarrow & -120x \color{red}{-15} \color{blue}{+15} \color{blue}{+64x} & = & \color{red}{-64x} +3 \color{blue}{+64x} \color{blue}{+15} \\\Leftrightarrow & -120x+64x& = & 3+15 \\\Leftrightarrow & \color{red}{-56} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-56} & & \\\Leftrightarrow & x = \frac{-9}{28} & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & 9x+\frac{5}{8} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{-80} & = & \color{red}{504x} +35 \\\Leftrightarrow & 560x \color{red}{-80} \color{blue}{+80} \color{blue}{-504x} & = & \color{red}{504x} +35 \color{blue}{-504x} \color{blue}{+80} \\\Leftrightarrow & 560x-504x& = & 35+80 \\\Leftrightarrow & \color{red}{56} x& = & 115 \\\Leftrightarrow & x = \frac{115}{56} & & \\ & V = \left\{ \frac{115}{56} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{8})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{-45} & = & \color{red}{-192x} +80 \\\Leftrightarrow & -360x \color{red}{-45} \color{blue}{+45} \color{blue}{+192x} & = & \color{red}{-192x} +80 \color{blue}{+192x} \color{blue}{+45} \\\Leftrightarrow & -360x+192x& = & 80+45 \\\Leftrightarrow & \color{red}{-168} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-168} & & \\\Leftrightarrow & x = \frac{-125}{168} & & \\ & V = \left\{ \frac{-125}{168} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{-441x} +56 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & 378x+441x& = & 56+90 \\\Leftrightarrow & \color{red}{819} x& = & 146 \\\Leftrightarrow & x = \frac{146}{819} & & \\ & V = \left\{ \frac{146}{819} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{7})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -9x+\frac{9}{7}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+45} & = & \color{red}{175x} +49 \\\Leftrightarrow & -315x \color{red}{+45} \color{blue}{-45} \color{blue}{-175x} & = & \color{red}{175x} +49 \color{blue}{-175x} \color{blue}{-45} \\\Leftrightarrow & -315x-175x& = & 49-45 \\\Leftrightarrow & \color{red}{-490} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-490} & & \\\Leftrightarrow & x = \frac{-2}{245} & & \\ & V = \left\{ \frac{-2}{245} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-600}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -600x \color{red}{-48} & = & \color{red}{140x} +35 \\\Leftrightarrow & -600x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & -600x-140x& = & 35+48 \\\Leftrightarrow & \color{red}{-740} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-740} & & \\\Leftrightarrow & x = \frac{-83}{740} & & \\ & V = \left\{ \frac{-83}{740} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{5})& = & 9x+\frac{5}{8} \\\Leftrightarrow & 14x-\frac{21}{5}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x- \frac{168}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{-168} & = & \color{red}{360x} +25 \\\Leftrightarrow & 560x \color{red}{-168} \color{blue}{+168} \color{blue}{-360x} & = & \color{red}{360x} +25 \color{blue}{-360x} \color{blue}{+168} \\\Leftrightarrow & 560x-360x& = & 25+168 \\\Leftrightarrow & \color{red}{200} x& = & 193 \\\Leftrightarrow & x = \frac{193}{200} & & \\ & V = \left\{ \frac{193}{200} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{+24} & = & \color{red}{84x} +63 \\\Leftrightarrow & -224x \color{red}{+24} \color{blue}{-24} \color{blue}{-84x} & = & \color{red}{84x} +63 \color{blue}{-84x} \color{blue}{-24} \\\Leftrightarrow & -224x-84x& = & 63-24 \\\Leftrightarrow & \color{red}{-308} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-308} & & \\\Leftrightarrow & x = \frac{-39}{308} & & \\ & V = \left\{ \frac{-39}{308} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & 9x+\frac{3}{5} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 9x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{+12} & = & \color{red}{45x} +3 \\\Leftrightarrow & 80x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +3 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & 80x-45x& = & 3-12 \\\Leftrightarrow & \color{red}{35} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{35} & & \\ & V = \left\{ \frac{-9}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+84} & = & \color{red}{105x} +50 \\\Leftrightarrow & 700x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & 700x-105x& = & 50-84 \\\Leftrightarrow & \color{red}{595} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{595} & & \\\Leftrightarrow & x = \frac{-2}{35} & & \\ & V = \left\{ \frac{-2}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-16} & = & \color{red}{49x} +4 \\\Leftrightarrow & -112x \color{red}{-16} \color{blue}{+16} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{+16} \\\Leftrightarrow & -112x-49x& = & 4+16 \\\Leftrightarrow & \color{red}{-161} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-161} & & \\\Leftrightarrow & x = \frac{-20}{161} & & \\ & V = \left\{ \frac{-20}{161} \right\} & \\\end{align}\)