Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{36}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 36x \color{red}{+16} & = & \color{red}{-30x} +9 \\\Leftrightarrow & 36x \color{red}{+16} \color{blue}{-16} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{-16} \\\Leftrightarrow & 36x+30x& = & 9-16 \\\Leftrightarrow & \color{red}{66} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{66} & & \\ & V = \left\{ \frac{-7}{66} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+10} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -140x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -140x+49x& = & 10-10 \\\Leftrightarrow & \color{red}{-91} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-91} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{5})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -14x+\frac{28}{5}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x+ \frac{28}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{+28} & = & \color{red}{15x} +4 \\\Leftrightarrow & -70x \color{red}{+28} \color{blue}{-28} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{-28} \\\Leftrightarrow & -70x-15x& = & 4-28 \\\Leftrightarrow & \color{red}{-85} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-85} & & \\\Leftrightarrow & x = \frac{24}{85} & & \\ & V = \left\{ \frac{24}{85} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+84} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -840x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & -840x+175x& = & 50-84 \\\Leftrightarrow & \color{red}{-665} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-665} & & \\\Leftrightarrow & x = \frac{34}{665} & & \\ & V = \left\{ \frac{34}{665} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-18} & = & \color{red}{189x} +70 \\\Leftrightarrow & -168x \color{red}{-18} \color{blue}{+18} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{+18} \\\Leftrightarrow & -168x-189x& = & 70+18 \\\Leftrightarrow & \color{red}{-357} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-357} & & \\\Leftrightarrow & x = \frac{-88}{357} & & \\ & V = \left\{ \frac{-88}{357} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{7})& = & -5x+\frac{5}{12} \\\Leftrightarrow & 12x+\frac{20}{7}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1008}{ \color{blue}{84} }x+ \frac{240}{ \color{blue}{84} })& = & (\frac{-420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1008x \color{red}{+240} & = & \color{red}{-420x} +35 \\\Leftrightarrow & 1008x \color{red}{+240} \color{blue}{-240} \color{blue}{+420x} & = & \color{red}{-420x} +35 \color{blue}{+420x} \color{blue}{-240} \\\Leftrightarrow & 1008x+420x& = & 35-240 \\\Leftrightarrow & \color{red}{1428} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{1428} & & \\ & V = \left\{ \frac{-205}{1428} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 24x-\frac{24}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{165x} +88 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+72} \\\Leftrightarrow & 792x-165x& = & 88+72 \\\Leftrightarrow & \color{red}{627} x& = & 160 \\\Leftrightarrow & x = \frac{160}{627} & & \\ & V = \left\{ \frac{160}{627} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & 2x+\frac{7}{2} \\\Leftrightarrow & 35x+\frac{7}{3}& = & 2x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{14}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+14} & = & \color{red}{12x} +21 \\\Leftrightarrow & 210x \color{red}{+14} \color{blue}{-14} \color{blue}{-12x} & = & \color{red}{12x} +21 \color{blue}{-12x} \color{blue}{-14} \\\Leftrightarrow & 210x-12x& = & 21-14 \\\Leftrightarrow & \color{red}{198} x& = & 7 \\\Leftrightarrow & x = \frac{7}{198} & & \\ & V = \left\{ \frac{7}{198} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{-24} & = & \color{red}{-80x} +9 \\\Leftrightarrow & -150x \color{red}{-24} \color{blue}{+24} \color{blue}{+80x} & = & \color{red}{-80x} +9 \color{blue}{+80x} \color{blue}{+24} \\\Leftrightarrow & -150x+80x& = & 9+24 \\\Leftrightarrow & \color{red}{-70} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-70} & & \\\Leftrightarrow & x = \frac{-33}{70} & & \\ & V = \left\{ \frac{-33}{70} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{10}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-30} & = & \color{red}{231x} +44 \\\Leftrightarrow & -660x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & -660x-231x& = & 44+30 \\\Leftrightarrow & \color{red}{-891} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-891} & & \\\Leftrightarrow & x = \frac{-74}{891} & & \\ & V = \left\{ \frac{-74}{891} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 16x+\frac{8}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{+16} & = & \color{red}{18x} +21 \\\Leftrightarrow & 96x \color{red}{+16} \color{blue}{-16} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{-16} \\\Leftrightarrow & 96x-18x& = & 21-16 \\\Leftrightarrow & \color{red}{78} x& = & 5 \\\Leftrightarrow & x = \frac{5}{78} & & \\ & V = \left\{ \frac{5}{78} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{3})& = & 7x+\frac{7}{12} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{+80} & = & \color{red}{84x} +7 \\\Leftrightarrow & 120x \color{red}{+80} \color{blue}{-80} \color{blue}{-84x} & = & \color{red}{84x} +7 \color{blue}{-84x} \color{blue}{-80} \\\Leftrightarrow & 120x-84x& = & 7-80 \\\Leftrightarrow & \color{red}{36} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{36} & & \\ & V = \left\{ \frac{-73}{36} \right\} & \\\end{align}\)