Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{648}{ \color{blue}{72} }x+ \frac{56}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{-189} & = & \color{red}{648x} +56 \\\Leftrightarrow & 2016x \color{red}{-189} \color{blue}{+189} \color{blue}{-648x} & = & \color{red}{648x} +56 \color{blue}{-648x} \color{blue}{+189} \\\Leftrightarrow & 2016x-648x& = & 56+189 \\\Leftrightarrow & \color{red}{1368} x& = & 245 \\\Leftrightarrow & x = \frac{245}{1368} & & \\ & V = \left\{ \frac{245}{1368} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{11})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 9x+\frac{6}{11}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{+6} & = & \color{red}{77x} +3 \\\Leftrightarrow & 99x \color{red}{+6} \color{blue}{-6} \color{blue}{-77x} & = & \color{red}{77x} +3 \color{blue}{-77x} \color{blue}{-6} \\\Leftrightarrow & 99x-77x& = & 3-6 \\\Leftrightarrow & \color{red}{22} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{22} & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2640}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2640x \color{red}{-180} & = & \color{red}{550x} +33 \\\Leftrightarrow & 2640x \color{red}{-180} \color{blue}{+180} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{+180} \\\Leftrightarrow & 2640x-550x& = & 33+180 \\\Leftrightarrow & \color{red}{2090} x& = & 213 \\\Leftrightarrow & x = \frac{213}{2090} & & \\ & V = \left\{ \frac{213}{2090} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+60} & = & \color{red}{275x} +66 \\\Leftrightarrow & 660x \color{red}{+60} \color{blue}{-60} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-60} \\\Leftrightarrow & 660x-275x& = & 66-60 \\\Leftrightarrow & \color{red}{385} x& = & 6 \\\Leftrightarrow & x = \frac{6}{385} & & \\ & V = \left\{ \frac{6}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{7}{11} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+264} & = & \color{red}{385x} +35 \\\Leftrightarrow & 1650x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & 1650x-385x& = & 35-264 \\\Leftrightarrow & \color{red}{1265} x& = & -229 \\\Leftrightarrow & x = \frac{-229}{1265} & & \\ & V = \left\{ \frac{-229}{1265} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{12})& = & 4x+\frac{7}{9} \\\Leftrightarrow & 25x-\frac{25}{12}& = & 4x+\frac{7}{9} \\ & & & \text{kgv van noemers 12 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{900}{ \color{blue}{36} }x- \frac{75}{ \color{blue}{36} })& = & (\frac{144}{ \color{blue}{36} }x+ \frac{28}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 900x \color{red}{-75} & = & \color{red}{144x} +28 \\\Leftrightarrow & 900x \color{red}{-75} \color{blue}{+75} \color{blue}{-144x} & = & \color{red}{144x} +28 \color{blue}{-144x} \color{blue}{+75} \\\Leftrightarrow & 900x-144x& = & 28+75 \\\Leftrightarrow & \color{red}{756} x& = & 103 \\\Leftrightarrow & x = \frac{103}{756} & & \\ & V = \left\{ \frac{103}{756} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{189x} +56 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{-90} \\\Leftrightarrow & -378x-189x& = & 56-90 \\\Leftrightarrow & \color{red}{-567} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-567} & & \\\Leftrightarrow & x = \frac{34}{567} & & \\ & V = \left\{ \frac{34}{567} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+330} & = & \color{red}{539x} +42 \\\Leftrightarrow & 1848x \color{red}{+330} \color{blue}{-330} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{-330} \\\Leftrightarrow & 1848x-539x& = & 42-330 \\\Leftrightarrow & \color{red}{1309} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{1309} & & \\ & V = \left\{ \frac{-288}{1309} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{3})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 6x+\frac{4}{3}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+28} & = & \color{red}{105x} +18 \\\Leftrightarrow & 126x \color{red}{+28} \color{blue}{-28} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-28} \\\Leftrightarrow & 126x-105x& = & 18-28 \\\Leftrightarrow & \color{red}{21} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & 5x+\frac{7}{6} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1008}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1008x \color{red}{-180} & = & \color{red}{210x} +49 \\\Leftrightarrow & -1008x \color{red}{-180} \color{blue}{+180} \color{blue}{-210x} & = & \color{red}{210x} +49 \color{blue}{-210x} \color{blue}{+180} \\\Leftrightarrow & -1008x-210x& = & 49+180 \\\Leftrightarrow & \color{red}{-1218} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-1218} & & \\\Leftrightarrow & x = \frac{-229}{1218} & & \\ & V = \left\{ \frac{-229}{1218} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-96} & = & \color{red}{-200x} +35 \\\Leftrightarrow & 480x \color{red}{-96} \color{blue}{+96} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{+96} \\\Leftrightarrow & 480x+200x& = & 35+96 \\\Leftrightarrow & \color{red}{680} x& = & 131 \\\Leftrightarrow & x = \frac{131}{680} & & \\ & V = \left\{ \frac{131}{680} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{11})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{10}{11}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+30} & = & \color{red}{-297x} +110 \\\Leftrightarrow & -264x \color{red}{+30} \color{blue}{-30} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{-30} \\\Leftrightarrow & -264x+297x& = & 110-30 \\\Leftrightarrow & \color{red}{33} x& = & 80 \\\Leftrightarrow & x = \frac{80}{33} & & \\ & V = \left\{ \frac{80}{33} \right\} & \\\end{align}\)