Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -4x-\frac{8}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-8} & = & \color{red}{35x} +8 \\\Leftrightarrow & -28x \color{red}{-8} \color{blue}{+8} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+8} \\\Leftrightarrow & -28x-35x& = & 8+8 \\\Leftrightarrow & \color{red}{-63} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-63} & & \\\Leftrightarrow & x = \frac{-16}{63} & & \\ & V = \left\{ \frac{-16}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 8x-\frac{4}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{20}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-20} & = & \color{red}{-245x} +14 \\\Leftrightarrow & 280x \color{red}{-20} \color{blue}{+20} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{+20} \\\Leftrightarrow & 280x+245x& = & 14+20 \\\Leftrightarrow & \color{red}{525} x& = & 34 \\\Leftrightarrow & x = \frac{34}{525} & & \\ & V = \left\{ \frac{34}{525} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{8})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{+231} & = & \color{red}{264x} +48 \\\Leftrightarrow & 3080x \color{red}{+231} \color{blue}{-231} \color{blue}{-264x} & = & \color{red}{264x} +48 \color{blue}{-264x} \color{blue}{-231} \\\Leftrightarrow & 3080x-264x& = & 48-231 \\\Leftrightarrow & \color{red}{2816} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{2816} & & \\ & V = \left\{ \frac{-183}{2816} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+6} & = & \color{red}{-77x} +9 \\\Leftrightarrow & 66x \color{red}{+6} \color{blue}{-6} \color{blue}{+77x} & = & \color{red}{-77x} +9 \color{blue}{+77x} \color{blue}{-6} \\\Leftrightarrow & 66x+77x& = & 9-6 \\\Leftrightarrow & \color{red}{143} x& = & 3 \\\Leftrightarrow & x = \frac{3}{143} & & \\ & V = \left\{ \frac{3}{143} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{-40} & = & \color{red}{-308x} +99 \\\Leftrightarrow & -440x \color{red}{-40} \color{blue}{+40} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+40} \\\Leftrightarrow & -440x+308x& = & 99+40 \\\Leftrightarrow & \color{red}{-132} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-132} & & \\\Leftrightarrow & x = \frac{-139}{132} & & \\ & V = \left\{ \frac{-139}{132} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+88} & = & \color{red}{693x} +36 \\\Leftrightarrow & 792x \color{red}{+88} \color{blue}{-88} \color{blue}{-693x} & = & \color{red}{693x} +36 \color{blue}{-693x} \color{blue}{-88} \\\Leftrightarrow & 792x-693x& = & 36-88 \\\Leftrightarrow & \color{red}{99} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{99} & & \\ & V = \left\{ \frac{-52}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{8})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -28x-\frac{35}{8}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2016}{ \color{blue}{72} }x- \frac{315}{ \color{blue}{72} })& = & (\frac{360}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2016x \color{red}{-315} & = & \color{red}{360x} +16 \\\Leftrightarrow & -2016x \color{red}{-315} \color{blue}{+315} \color{blue}{-360x} & = & \color{red}{360x} +16 \color{blue}{-360x} \color{blue}{+315} \\\Leftrightarrow & -2016x-360x& = & 16+315 \\\Leftrightarrow & \color{red}{-2376} x& = & 331 \\\Leftrightarrow & x = \frac{331}{-2376} & & \\\Leftrightarrow & x = \frac{-331}{2376} & & \\ & V = \left\{ \frac{-331}{2376} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-45} & = & \color{red}{84x} +32 \\\Leftrightarrow & -240x \color{red}{-45} \color{blue}{+45} \color{blue}{-84x} & = & \color{red}{84x} +32 \color{blue}{-84x} \color{blue}{+45} \\\Leftrightarrow & -240x-84x& = & 32+45 \\\Leftrightarrow & \color{red}{-324} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-324} & & \\\Leftrightarrow & x = \frac{-77}{324} & & \\ & V = \left\{ \frac{-77}{324} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 12x+\frac{6}{5}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+6} & = & \color{red}{25x} +3 \\\Leftrightarrow & 60x \color{red}{+6} \color{blue}{-6} \color{blue}{-25x} & = & \color{red}{25x} +3 \color{blue}{-25x} \color{blue}{-6} \\\Leftrightarrow & 60x-25x& = & 3-6 \\\Leftrightarrow & \color{red}{35} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{35} & & \\ & V = \left\{ \frac{-3}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+24} & = & \color{red}{-90x} +35 \\\Leftrightarrow & -80x \color{red}{+24} \color{blue}{-24} \color{blue}{+90x} & = & \color{red}{-90x} +35 \color{blue}{+90x} \color{blue}{-24} \\\Leftrightarrow & -80x+90x& = & 35-24 \\\Leftrightarrow & \color{red}{10} x& = & 11 \\\Leftrightarrow & x = \frac{11}{10} & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -60x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{-35} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-35} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-28} & = & \color{red}{105x} +20 \\\Leftrightarrow & 140x \color{red}{-28} \color{blue}{+28} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+28} \\\Leftrightarrow & 140x-105x& = & 20+28 \\\Leftrightarrow & \color{red}{35} x& = & 48 \\\Leftrightarrow & x = \frac{48}{35} & & \\ & V = \left\{ \frac{48}{35} \right\} & \\\end{align}\)