Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{6}{11}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-264}{ \color{blue}{66} }x+ \frac{36}{ \color{blue}{66} })& = & (\frac{-594}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -264x \color{red}{+36} & = & \color{red}{-594x} +55 \\\Leftrightarrow & -264x \color{red}{+36} \color{blue}{-36} \color{blue}{+594x} & = & \color{red}{-594x} +55 \color{blue}{+594x} \color{blue}{-36} \\\Leftrightarrow & -264x+594x& = & 55-36 \\\Leftrightarrow & \color{red}{330} x& = & 19 \\\Leftrightarrow & x = \frac{19}{330} & & \\ & V = \left\{ \frac{19}{330} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{7})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{15}{7}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+45} & = & \color{red}{-63x} +28 \\\Leftrightarrow & 210x \color{red}{+45} \color{blue}{-45} \color{blue}{+63x} & = & \color{red}{-63x} +28 \color{blue}{+63x} \color{blue}{-45} \\\Leftrightarrow & 210x+63x& = & 28-45 \\\Leftrightarrow & \color{red}{273} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{273} & & \\ & V = \left\{ \frac{-17}{273} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 24x-\frac{30}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-210} & = & \color{red}{385x} +88 \\\Leftrightarrow & 1848x \color{red}{-210} \color{blue}{+210} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+210} \\\Leftrightarrow & 1848x-385x& = & 88+210 \\\Leftrightarrow & \color{red}{1463} x& = & 298 \\\Leftrightarrow & x = \frac{298}{1463} & & \\ & V = \left\{ \frac{298}{1463} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{24}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{35x} +6 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & 120x-35x& = & 6+24 \\\Leftrightarrow & \color{red}{85} x& = & 30 \\\Leftrightarrow & x = \frac{30}{85} & & \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{7}{10} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{14}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-75} & = & \color{red}{100x} +14 \\\Leftrightarrow & -240x \color{red}{-75} \color{blue}{+75} \color{blue}{-100x} & = & \color{red}{100x} +14 \color{blue}{-100x} \color{blue}{+75} \\\Leftrightarrow & -240x-100x& = & 14+75 \\\Leftrightarrow & \color{red}{-340} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-340} & & \\\Leftrightarrow & x = \frac{-89}{340} & & \\ & V = \left\{ \frac{-89}{340} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+10} & = & \color{red}{-21x} +4 \\\Leftrightarrow & 70x \color{red}{+10} \color{blue}{-10} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{-10} \\\Leftrightarrow & 70x+21x& = & 4-10 \\\Leftrightarrow & \color{red}{91} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{91} & & \\ & V = \left\{ \frac{-6}{91} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{2})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 6x+\frac{9}{2}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{24}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 24x \color{red}{+18} & = & \color{red}{20x} +3 \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{-20x} & = & \color{red}{20x} +3 \color{blue}{-20x} \color{blue}{-18} \\\Leftrightarrow & 24x-20x& = & 3-18 \\\Leftrightarrow & \color{red}{4} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{4} & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{-162} & = & \color{red}{693x} +88 \\\Leftrightarrow & -2970x \color{red}{-162} \color{blue}{+162} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{+162} \\\Leftrightarrow & -2970x-693x& = & 88+162 \\\Leftrightarrow & \color{red}{-3663} x& = & 250 \\\Leftrightarrow & x = \frac{250}{-3663} & & \\\Leftrightarrow & x = \frac{-250}{3663} & & \\ & V = \left\{ \frac{-250}{3663} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-154} & = & \color{red}{99x} +12 \\\Leftrightarrow & -1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-99x} & = & \color{red}{99x} +12 \color{blue}{-99x} \color{blue}{+154} \\\Leftrightarrow & -1155x-99x& = & 12+154 \\\Leftrightarrow & \color{red}{-1254} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-1254} & & \\\Leftrightarrow & x = \frac{-83}{627} & & \\ & V = \left\{ \frac{-83}{627} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-24} & = & \color{red}{90x} +35 \\\Leftrightarrow & -80x \color{red}{-24} \color{blue}{+24} \color{blue}{-90x} & = & \color{red}{90x} +35 \color{blue}{-90x} \color{blue}{+24} \\\Leftrightarrow & -80x-90x& = & 35+24 \\\Leftrightarrow & \color{red}{-170} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-170} & & \\\Leftrightarrow & x = \frac{-59}{170} & & \\ & V = \left\{ \frac{-59}{170} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & -4x+\frac{7}{2} \\\Leftrightarrow & -15x-\frac{15}{11}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{-88x} +77 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{+88x} & = & \color{red}{-88x} +77 \color{blue}{+88x} \color{blue}{+30} \\\Leftrightarrow & -330x+88x& = & 77+30 \\\Leftrightarrow & \color{red}{-242} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-242} & & \\\Leftrightarrow & x = \frac{-107}{242} & & \\ & V = \left\{ \frac{-107}{242} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -6x+\frac{4}{9} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -6x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{900}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-216}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 900x \color{red}{+135} & = & \color{red}{-216x} +16 \\\Leftrightarrow & 900x \color{red}{+135} \color{blue}{-135} \color{blue}{+216x} & = & \color{red}{-216x} +16 \color{blue}{+216x} \color{blue}{-135} \\\Leftrightarrow & 900x+216x& = & 16-135 \\\Leftrightarrow & \color{red}{1116} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{1116} & & \\ & V = \left\{ \frac{-119}{1116} \right\} & \\\end{align}\)