Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{24}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{72}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-72} & = & \color{red}{147x} +56 \\\Leftrightarrow & 252x \color{red}{-72} \color{blue}{+72} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+72} \\\Leftrightarrow & 252x-147x& = & 56+72 \\\Leftrightarrow & \color{red}{105} x& = & 128 \\\Leftrightarrow & x = \frac{128}{105} & & \\ & V = \left\{ \frac{128}{105} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -8x+\frac{3}{10} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1750}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-560}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1750x \color{red}{+100} & = & \color{red}{-560x} +21 \\\Leftrightarrow & 1750x \color{red}{+100} \color{blue}{-100} \color{blue}{+560x} & = & \color{red}{-560x} +21 \color{blue}{+560x} \color{blue}{-100} \\\Leftrightarrow & 1750x+560x& = & 21-100 \\\Leftrightarrow & \color{red}{2310} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{2310} & & \\ & V = \left\{ \frac{-79}{2310} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-90} & = & \color{red}{-275x} +88 \\\Leftrightarrow & -1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +88 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -1320x+275x& = & 88+90 \\\Leftrightarrow & \color{red}{-1045} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-1045} & & \\\Leftrightarrow & x = \frac{-178}{1045} & & \\ & V = \left\{ \frac{-178}{1045} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+6} & = & \color{red}{35x} +2 \\\Leftrightarrow & 42x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & 42x-35x& = & 2-6 \\\Leftrightarrow & \color{red}{7} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -24x-\frac{24}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-168} & = & \color{red}{539x} +88 \\\Leftrightarrow & -1848x \color{red}{-168} \color{blue}{+168} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{+168} \\\Leftrightarrow & -1848x-539x& = & 88+168 \\\Leftrightarrow & \color{red}{-2387} x& = & 256 \\\Leftrightarrow & x = \frac{256}{-2387} & & \\\Leftrightarrow & x = \frac{-256}{2387} & & \\ & V = \left\{ \frac{-256}{2387} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+176} & = & \color{red}{539x} +28 \\\Leftrightarrow & 1232x \color{red}{+176} \color{blue}{-176} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{-176} \\\Leftrightarrow & 1232x-539x& = & 28-176 \\\Leftrightarrow & \color{red}{693} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{693} & & \\ & V = \left\{ \frac{-148}{693} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{2}{9} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1512}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1512x \color{red}{-189} & = & \color{red}{576x} +16 \\\Leftrightarrow & -1512x \color{red}{-189} \color{blue}{+189} \color{blue}{-576x} & = & \color{red}{576x} +16 \color{blue}{-576x} \color{blue}{+189} \\\Leftrightarrow & -1512x-576x& = & 16+189 \\\Leftrightarrow & \color{red}{-2088} x& = & 205 \\\Leftrightarrow & x = \frac{205}{-2088} & & \\\Leftrightarrow & x = \frac{-205}{2088} & & \\ & V = \left\{ \frac{-205}{2088} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -12x-\frac{30}{11}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-150} & = & \color{red}{275x} +77 \\\Leftrightarrow & -660x \color{red}{-150} \color{blue}{+150} \color{blue}{-275x} & = & \color{red}{275x} +77 \color{blue}{-275x} \color{blue}{+150} \\\Leftrightarrow & -660x-275x& = & 77+150 \\\Leftrightarrow & \color{red}{-935} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-935} & & \\\Leftrightarrow & x = \frac{-227}{935} & & \\ & V = \left\{ \frac{-227}{935} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-18} & = & \color{red}{-147x} +28 \\\Leftrightarrow & 315x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & 315x+147x& = & 28+18 \\\Leftrightarrow & \color{red}{462} x& = & 46 \\\Leftrightarrow & x = \frac{46}{462} & & \\\Leftrightarrow & x = \frac{23}{231} & & \\ & V = \left\{ \frac{23}{231} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{+70} & = & \color{red}{-135x} +18 \\\Leftrightarrow & 210x \color{red}{+70} \color{blue}{-70} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-70} \\\Leftrightarrow & 210x+135x& = & 18-70 \\\Leftrightarrow & \color{red}{345} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{345} & & \\ & V = \left\{ \frac{-52}{345} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{448}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 448x \color{red}{+64} & = & \color{red}{-84x} +21 \\\Leftrightarrow & 448x \color{red}{+64} \color{blue}{-64} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{-64} \\\Leftrightarrow & 448x+84x& = & 21-64 \\\Leftrightarrow & \color{red}{532} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{532} & & \\ & V = \left\{ \frac{-43}{532} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{4})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{+105} & = & \color{red}{140x} +8 \\\Leftrightarrow & -336x \color{red}{+105} \color{blue}{-105} \color{blue}{-140x} & = & \color{red}{140x} +8 \color{blue}{-140x} \color{blue}{-105} \\\Leftrightarrow & -336x-140x& = & 8-105 \\\Leftrightarrow & \color{red}{-476} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-476} & & \\\Leftrightarrow & x = \frac{97}{476} & & \\ & V = \left\{ \frac{97}{476} \right\} & \\\end{align}\)