Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{24}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{48}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-48} & = & \color{red}{110x} +99 \\\Leftrightarrow & 264x \color{red}{-48} \color{blue}{+48} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{+48} \\\Leftrightarrow & 264x-110x& = & 99+48 \\\Leftrightarrow & \color{red}{154} x& = & 147 \\\Leftrightarrow & x = \frac{147}{154} & & \\\Leftrightarrow & x = \frac{21}{22} & & \\ & V = \left\{ \frac{21}{22} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{504}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 504x \color{red}{-36} & = & \color{red}{-210x} +49 \\\Leftrightarrow & 504x \color{red}{-36} \color{blue}{+36} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{+36} \\\Leftrightarrow & 504x+210x& = & 49+36 \\\Leftrightarrow & \color{red}{714} x& = & 85 \\\Leftrightarrow & x = \frac{85}{714} & & \\\Leftrightarrow & x = \frac{5}{42} & & \\ & V = \left\{ \frac{5}{42} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{11})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1584}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1584x \color{red}{-144} & = & \color{red}{-616x} +77 \\\Leftrightarrow & -1584x \color{red}{-144} \color{blue}{+144} \color{blue}{+616x} & = & \color{red}{-616x} +77 \color{blue}{+616x} \color{blue}{+144} \\\Leftrightarrow & -1584x+616x& = & 77+144 \\\Leftrightarrow & \color{red}{-968} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-968} & & \\\Leftrightarrow & x = \frac{-221}{968} & & \\ & V = \left\{ \frac{-221}{968} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 12x+\frac{24}{11}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+168} & = & \color{red}{385x} +66 \\\Leftrightarrow & 924x \color{red}{+168} \color{blue}{-168} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-168} \\\Leftrightarrow & 924x-385x& = & 66-168 \\\Leftrightarrow & \color{red}{539} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{539} & & \\ & V = \left\{ \frac{-102}{539} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-110} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -462x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -462x+539x& = & 28+110 \\\Leftrightarrow & \color{red}{77} x& = & 138 \\\Leftrightarrow & x = \frac{138}{77} & & \\ & V = \left\{ \frac{138}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{7})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -15x+\frac{25}{7}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{25}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+25} & = & \color{red}{-56x} +9 \\\Leftrightarrow & -105x \color{red}{+25} \color{blue}{-25} \color{blue}{+56x} & = & \color{red}{-56x} +9 \color{blue}{+56x} \color{blue}{-25} \\\Leftrightarrow & -105x+56x& = & 9-25 \\\Leftrightarrow & \color{red}{-49} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-49} & & \\\Leftrightarrow & x = \frac{16}{49} & & \\ & V = \left\{ \frac{16}{49} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{-45x} +24 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{+45x} & = & \color{red}{-45x} +24 \color{blue}{+45x} \color{blue}{-140} \\\Leftrightarrow & 420x+45x& = & 24-140 \\\Leftrightarrow & \color{red}{465} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{465} & & \\ & V = \left\{ \frac{-116}{465} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{15}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+45} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 198x \color{red}{+45} \color{blue}{-45} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-45} \\\Leftrightarrow & 198x+165x& = & 22-45 \\\Leftrightarrow & \color{red}{363} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{363} & & \\ & V = \left\{ \frac{-23}{363} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{189x} +56 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{+30} \\\Leftrightarrow & 210x-189x& = & 56+30 \\\Leftrightarrow & \color{red}{21} x& = & 86 \\\Leftrightarrow & x = \frac{86}{21} & & \\ & V = \left\{ \frac{86}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{11})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -10x-\frac{20}{11}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1100}{ \color{blue}{110} }x- \frac{200}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1100x \color{red}{-200} & = & \color{red}{770x} +33 \\\Leftrightarrow & -1100x \color{red}{-200} \color{blue}{+200} \color{blue}{-770x} & = & \color{red}{770x} +33 \color{blue}{-770x} \color{blue}{+200} \\\Leftrightarrow & -1100x-770x& = & 33+200 \\\Leftrightarrow & \color{red}{-1870} x& = & 233 \\\Leftrightarrow & x = \frac{233}{-1870} & & \\\Leftrightarrow & x = \frac{-233}{1870} & & \\ & V = \left\{ \frac{-233}{1870} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & -630x+147x& = & 28+90 \\\Leftrightarrow & \color{red}{-483} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-483} & & \\\Leftrightarrow & x = \frac{-118}{483} & & \\ & V = \left\{ \frac{-118}{483} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -8x-\frac{20}{3}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-96}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{-80} & = & \color{red}{-108x} +9 \\\Leftrightarrow & -96x \color{red}{-80} \color{blue}{+80} \color{blue}{+108x} & = & \color{red}{-108x} +9 \color{blue}{+108x} \color{blue}{+80} \\\Leftrightarrow & -96x+108x& = & 9+80 \\\Leftrightarrow & \color{red}{12} x& = & 89 \\\Leftrightarrow & x = \frac{89}{12} & & \\ & V = \left\{ \frac{89}{12} \right\} & \\\end{align}\)