Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 18x-\frac{24}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{72}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-72} & = & \color{red}{147x} +56 \\\Leftrightarrow & 378x \color{red}{-72} \color{blue}{+72} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+72} \\\Leftrightarrow & 378x-147x& = & 56+72 \\\Leftrightarrow & \color{red}{231} x& = & 128 \\\Leftrightarrow & x = \frac{128}{231} & & \\ & V = \left\{ \frac{128}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{11})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{15}{11}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-30} & = & \color{red}{-66x} +55 \\\Leftrightarrow & 440x \color{red}{-30} \color{blue}{+30} \color{blue}{+66x} & = & \color{red}{-66x} +55 \color{blue}{+66x} \color{blue}{+30} \\\Leftrightarrow & 440x+66x& = & 55+30 \\\Leftrightarrow & \color{red}{506} x& = & 85 \\\Leftrightarrow & x = \frac{85}{506} & & \\ & V = \left\{ \frac{85}{506} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+2)& = & 2x+\frac{7}{4} \\\Leftrightarrow & 21x-14& = & 2x+\frac{7}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{84}{ \color{blue}{4} }x- \frac{56}{ \color{blue}{4} })& = & (\frac{8}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{8x} +7 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{-8x} & = & \color{red}{8x} +7 \color{blue}{-8x} \color{blue}{+56} \\\Leftrightarrow & 84x-8x& = & 7+56 \\\Leftrightarrow & \color{red}{76} x& = & 63 \\\Leftrightarrow & x = \frac{63}{76} & & \\ & V = \left\{ \frac{63}{76} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-4} & = & \color{red}{35x} +4 \\\Leftrightarrow & -30x \color{red}{-4} \color{blue}{+4} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{+4} \\\Leftrightarrow & -30x-35x& = & 4+4 \\\Leftrightarrow & \color{red}{-65} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-65} & & \\\Leftrightarrow & x = \frac{-8}{65} & & \\ & V = \left\{ \frac{-8}{65} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -9x-\frac{6}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{-12} & = & \color{red}{-98x} +49 \\\Leftrightarrow & -126x \color{red}{-12} \color{blue}{+12} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+12} \\\Leftrightarrow & -126x+98x& = & 49+12 \\\Leftrightarrow & \color{red}{-28} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-28} & & \\\Leftrightarrow & x = \frac{-61}{28} & & \\ & V = \left\{ \frac{-61}{28} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{175x} +14 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +14 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -420x-175x& = & 14-150 \\\Leftrightarrow & \color{red}{-595} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-595} & & \\\Leftrightarrow & x = \frac{8}{35} & & \\ & V = \left\{ \frac{8}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{2})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{15}{2}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-105} & = & \color{red}{-98x} +16 \\\Leftrightarrow & -280x \color{red}{-105} \color{blue}{+105} \color{blue}{+98x} & = & \color{red}{-98x} +16 \color{blue}{+98x} \color{blue}{+105} \\\Leftrightarrow & -280x+98x& = & 16+105 \\\Leftrightarrow & \color{red}{-182} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-182} & & \\\Leftrightarrow & x = \frac{-121}{182} & & \\ & V = \left\{ \frac{-121}{182} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{3})& = & 2x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{25}{3}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+275} & = & \color{red}{66x} +24 \\\Leftrightarrow & 495x \color{red}{+275} \color{blue}{-275} \color{blue}{-66x} & = & \color{red}{66x} +24 \color{blue}{-66x} \color{blue}{-275} \\\Leftrightarrow & 495x-66x& = & 24-275 \\\Leftrightarrow & \color{red}{429} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{429} & & \\ & V = \left\{ \frac{-251}{429} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x+\frac{4}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+44} & = & \color{red}{-693x} +45 \\\Leftrightarrow & -594x \color{red}{+44} \color{blue}{-44} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{-44} \\\Leftrightarrow & -594x+693x& = & 45-44 \\\Leftrightarrow & \color{red}{99} x& = & 1 \\\Leftrightarrow & x = \frac{1}{99} & & \\ & V = \left\{ \frac{1}{99} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{3})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-24} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 72x \color{red}{-24} \color{blue}{+24} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{+24} \\\Leftrightarrow & 72x+45x& = & 10+24 \\\Leftrightarrow & \color{red}{117} x& = & 34 \\\Leftrightarrow & x = \frac{34}{117} & & \\ & V = \left\{ \frac{34}{117} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{3})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 14x+\frac{35}{3}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+385} & = & \color{red}{297x} +18 \\\Leftrightarrow & 462x \color{red}{+385} \color{blue}{-385} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{-385} \\\Leftrightarrow & 462x-297x& = & 18-385 \\\Leftrightarrow & \color{red}{165} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{165} & & \\ & V = \left\{ \frac{-367}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+16} & = & \color{red}{42x} +27 \\\Leftrightarrow & -96x \color{red}{+16} \color{blue}{-16} \color{blue}{-42x} & = & \color{red}{42x} +27 \color{blue}{-42x} \color{blue}{-16} \\\Leftrightarrow & -96x-42x& = & 27-16 \\\Leftrightarrow & \color{red}{-138} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-138} & & \\\Leftrightarrow & x = \frac{-11}{138} & & \\ & V = \left\{ \frac{-11}{138} \right\} & \\\end{align}\)