Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{5})& = & -2x+\frac{9}{11} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -2x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{-308} & = & \color{red}{-110x} +45 \\\Leftrightarrow & 1155x \color{red}{-308} \color{blue}{+308} \color{blue}{+110x} & = & \color{red}{-110x} +45 \color{blue}{+110x} \color{blue}{+308} \\\Leftrightarrow & 1155x+110x& = & 45+308 \\\Leftrightarrow & \color{red}{1265} x& = & 353 \\\Leftrightarrow & x = \frac{353}{1265} & & \\ & V = \left\{ \frac{353}{1265} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{12})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -25x+\frac{25}{12}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 12 en 10 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1500}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{540}{ \color{blue}{60} }x+ \frac{18}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1500x \color{red}{+125} & = & \color{red}{540x} +18 \\\Leftrightarrow & -1500x \color{red}{+125} \color{blue}{-125} \color{blue}{-540x} & = & \color{red}{540x} +18 \color{blue}{-540x} \color{blue}{-125} \\\Leftrightarrow & -1500x-540x& = & 18-125 \\\Leftrightarrow & \color{red}{-2040} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-2040} & & \\\Leftrightarrow & x = \frac{107}{2040} & & \\ & V = \left\{ \frac{107}{2040} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+110} & = & \color{red}{-231x} +35 \\\Leftrightarrow & -1540x \color{red}{+110} \color{blue}{-110} \color{blue}{+231x} & = & \color{red}{-231x} +35 \color{blue}{+231x} \color{blue}{-110} \\\Leftrightarrow & -1540x+231x& = & 35-110 \\\Leftrightarrow & \color{red}{-1309} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{-1309} & & \\\Leftrightarrow & x = \frac{75}{1309} & & \\ & V = \left\{ \frac{75}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{9})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 16x-\frac{20}{9}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{288}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 288x \color{red}{-40} & = & \color{red}{90x} +27 \\\Leftrightarrow & 288x \color{red}{-40} \color{blue}{+40} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{+40} \\\Leftrightarrow & 288x-90x& = & 27+40 \\\Leftrightarrow & \color{red}{198} x& = & 67 \\\Leftrightarrow & x = \frac{67}{198} & & \\ & V = \left\{ \frac{67}{198} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{4})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 20x-\frac{15}{4}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-135} & = & \color{red}{-252x} +8 \\\Leftrightarrow & 720x \color{red}{-135} \color{blue}{+135} \color{blue}{+252x} & = & \color{red}{-252x} +8 \color{blue}{+252x} \color{blue}{+135} \\\Leftrightarrow & 720x+252x& = & 8+135 \\\Leftrightarrow & \color{red}{972} x& = & 143 \\\Leftrightarrow & x = \frac{143}{972} & & \\ & V = \left\{ \frac{143}{972} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{9})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 10x-\frac{8}{9}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{-40} & = & \color{red}{315x} +72 \\\Leftrightarrow & 450x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +72 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & 450x-315x& = & 72+40 \\\Leftrightarrow & \color{red}{135} x& = & 112 \\\Leftrightarrow & x = \frac{112}{135} & & \\ & V = \left\{ \frac{112}{135} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{11})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 16x-\frac{16}{11}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-112} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 1232x \color{red}{-112} \color{blue}{+112} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+112} \\\Leftrightarrow & 1232x+231x& = & 22+112 \\\Leftrightarrow & \color{red}{1463} x& = & 134 \\\Leftrightarrow & x = \frac{134}{1463} & & \\ & V = \left\{ \frac{134}{1463} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+105} & = & \color{red}{-196x} +40 \\\Leftrightarrow & 700x \color{red}{+105} \color{blue}{-105} \color{blue}{+196x} & = & \color{red}{-196x} +40 \color{blue}{+196x} \color{blue}{-105} \\\Leftrightarrow & 700x+196x& = & 40-105 \\\Leftrightarrow & \color{red}{896} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{896} & & \\ & V = \left\{ \frac{-65}{896} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{1}{3})& = & 4x+\frac{2}{3} \\\Leftrightarrow & -28x+\frac{7}{3}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{+7} & = & \color{red}{12x} +2 \\\Leftrightarrow & -84x \color{red}{+7} \color{blue}{-7} \color{blue}{-12x} & = & \color{red}{12x} +2 \color{blue}{-12x} \color{blue}{-7} \\\Leftrightarrow & -84x-12x& = & 2-7 \\\Leftrightarrow & \color{red}{-96} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-96} & & \\\Leftrightarrow & x = \frac{5}{96} & & \\ & V = \left\{ \frac{5}{96} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+90} & = & \color{red}{105x} +28 \\\Leftrightarrow & -252x \color{red}{+90} \color{blue}{-90} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-90} \\\Leftrightarrow & -252x-105x& = & 28-90 \\\Leftrightarrow & \color{red}{-357} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-357} & & \\\Leftrightarrow & x = \frac{62}{357} & & \\ & V = \left\{ \frac{62}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{3})& = & -5x+\frac{4}{9} \\\Leftrightarrow & -28x+\frac{28}{3}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x+ \frac{84}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{+84} & = & \color{red}{-45x} +4 \\\Leftrightarrow & -252x \color{red}{+84} \color{blue}{-84} \color{blue}{+45x} & = & \color{red}{-45x} +4 \color{blue}{+45x} \color{blue}{-84} \\\Leftrightarrow & -252x+45x& = & 4-84 \\\Leftrightarrow & \color{red}{-207} x& = & -80 \\\Leftrightarrow & x = \frac{-80}{-207} & & \\\Leftrightarrow & x = \frac{80}{207} & & \\ & V = \left\{ \frac{80}{207} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{12}{11}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-60} & = & \color{red}{165x} +66 \\\Leftrightarrow & -1100x \color{red}{-60} \color{blue}{+60} \color{blue}{-165x} & = & \color{red}{165x} +66 \color{blue}{-165x} \color{blue}{+60} \\\Leftrightarrow & -1100x-165x& = & 66+60 \\\Leftrightarrow & \color{red}{-1265} x& = & 126 \\\Leftrightarrow & x = \frac{126}{-1265} & & \\\Leftrightarrow & x = \frac{-126}{1265} & & \\ & V = \left\{ \frac{-126}{1265} \right\} & \\\end{align}\)