Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{8})& = & -2x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{15}{8}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+45} & = & \color{red}{-48x} +64 \\\Leftrightarrow & -600x \color{red}{+45} \color{blue}{-45} \color{blue}{+48x} & = & \color{red}{-48x} +64 \color{blue}{+48x} \color{blue}{-45} \\\Leftrightarrow & -600x+48x& = & 64-45 \\\Leftrightarrow & \color{red}{-552} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-552} & & \\\Leftrightarrow & x = \frac{-19}{552} & & \\ & V = \left\{ \frac{-19}{552} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{7})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{10}{7}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-30} & = & \color{red}{-63x} +56 \\\Leftrightarrow & -168x \color{red}{-30} \color{blue}{+30} \color{blue}{+63x} & = & \color{red}{-63x} +56 \color{blue}{+63x} \color{blue}{+30} \\\Leftrightarrow & -168x+63x& = & 56+30 \\\Leftrightarrow & \color{red}{-105} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-105} & & \\\Leftrightarrow & x = \frac{-86}{105} & & \\ & V = \left\{ \frac{-86}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{9}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{27}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-27} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{-27} \color{blue}{+27} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+27} \\\Leftrightarrow & -126x-147x& = & 56+27 \\\Leftrightarrow & \color{red}{-273} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-273} & & \\\Leftrightarrow & x = \frac{-83}{273} & & \\ & V = \left\{ \frac{-83}{273} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-110} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 462x \color{red}{-110} \color{blue}{+110} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+110} \\\Leftrightarrow & 462x+385x& = & 14+110 \\\Leftrightarrow & \color{red}{847} x& = & 124 \\\Leftrightarrow & x = \frac{124}{847} & & \\ & V = \left\{ \frac{124}{847} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{-175x} +45 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & -420x+175x& = & 45-84 \\\Leftrightarrow & \color{red}{-245} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-245} & & \\\Leftrightarrow & x = \frac{39}{245} & & \\ & V = \left\{ \frac{39}{245} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+105} & = & \color{red}{196x} +40 \\\Leftrightarrow & -168x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +40 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & -168x-196x& = & 40-105 \\\Leftrightarrow & \color{red}{-364} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-364} & & \\\Leftrightarrow & x = \frac{5}{28} & & \\ & V = \left\{ \frac{5}{28} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{3})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 10x-\frac{10}{3}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x- \frac{100}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{-100} & = & \color{red}{-90x} +27 \\\Leftrightarrow & 300x \color{red}{-100} \color{blue}{+100} \color{blue}{+90x} & = & \color{red}{-90x} +27 \color{blue}{+90x} \color{blue}{+100} \\\Leftrightarrow & 300x+90x& = & 27+100 \\\Leftrightarrow & \color{red}{390} x& = & 127 \\\Leftrightarrow & x = \frac{127}{390} & & \\ & V = \left\{ \frac{127}{390} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{11})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 28x+\frac{28}{11}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{3696}{ \color{blue}{132} }x+ \frac{336}{ \color{blue}{132} })& = & (\frac{-396}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 3696x \color{red}{+336} & = & \color{red}{-396x} +55 \\\Leftrightarrow & 3696x \color{red}{+336} \color{blue}{-336} \color{blue}{+396x} & = & \color{red}{-396x} +55 \color{blue}{+396x} \color{blue}{-336} \\\Leftrightarrow & 3696x+396x& = & 55-336 \\\Leftrightarrow & \color{red}{4092} x& = & -281 \\\Leftrightarrow & x = \frac{-281}{4092} & & \\ & V = \left\{ \frac{-281}{4092} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{147x} +28 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & -126x-147x& = & 28-30 \\\Leftrightarrow & \color{red}{-273} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-273} & & \\\Leftrightarrow & x = \frac{2}{273} & & \\ & V = \left\{ \frac{2}{273} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{8})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{25}{8}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x- \frac{75}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{-75} & = & \color{red}{216x} +16 \\\Leftrightarrow & 480x \color{red}{-75} \color{blue}{+75} \color{blue}{-216x} & = & \color{red}{216x} +16 \color{blue}{-216x} \color{blue}{+75} \\\Leftrightarrow & 480x-216x& = & 16+75 \\\Leftrightarrow & \color{red}{264} x& = & 91 \\\Leftrightarrow & x = \frac{91}{264} & & \\ & V = \left\{ \frac{91}{264} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{7})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -10x-\frac{20}{7}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-840}{ \color{blue}{84} }x- \frac{240}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -840x \color{red}{-240} & = & \color{red}{588x} +49 \\\Leftrightarrow & -840x \color{red}{-240} \color{blue}{+240} \color{blue}{-588x} & = & \color{red}{588x} +49 \color{blue}{-588x} \color{blue}{+240} \\\Leftrightarrow & -840x-588x& = & 49+240 \\\Leftrightarrow & \color{red}{-1428} x& = & 289 \\\Leftrightarrow & x = \frac{289}{-1428} & & \\\Leftrightarrow & x = \frac{-17}{84} & & \\ & V = \left\{ \frac{-17}{84} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{5})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -6x-\frac{8}{5}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{8}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-8} & = & \color{red}{35x} +3 \\\Leftrightarrow & -30x \color{red}{-8} \color{blue}{+8} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+8} \\\Leftrightarrow & -30x-35x& = & 3+8 \\\Leftrightarrow & \color{red}{-65} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-65} & & \\\Leftrightarrow & x = \frac{-11}{65} & & \\ & V = \left\{ \frac{-11}{65} \right\} & \\\end{align}\)