Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x+\frac{12}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{+108} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -2970x \color{red}{+108} \color{blue}{-108} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{-108} \\\Leftrightarrow & -2970x+693x& = & 22-108 \\\Leftrightarrow & \color{red}{-2277} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-2277} & & \\\Leftrightarrow & x = \frac{86}{2277} & & \\ & V = \left\{ \frac{86}{2277} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -7x+\frac{5}{8} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{+15} & = & \color{red}{-56x} +5 \\\Leftrightarrow & -160x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +5 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -160x+56x& = & 5-15 \\\Leftrightarrow & \color{red}{-104} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-104} & & \\\Leftrightarrow & x = \frac{5}{52} & & \\ & V = \left\{ \frac{5}{52} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 12x+\frac{8}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+56} & = & \color{red}{175x} +45 \\\Leftrightarrow & 420x \color{red}{+56} \color{blue}{-56} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{-56} \\\Leftrightarrow & 420x-175x& = & 45-56 \\\Leftrightarrow & \color{red}{245} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{245} & & \\ & V = \left\{ \frac{-11}{245} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{9})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-140} & = & \color{red}{567x} +81 \\\Leftrightarrow & -1260x \color{red}{-140} \color{blue}{+140} \color{blue}{-567x} & = & \color{red}{567x} +81 \color{blue}{-567x} \color{blue}{+140} \\\Leftrightarrow & -1260x-567x& = & 81+140 \\\Leftrightarrow & \color{red}{-1827} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-1827} & & \\\Leftrightarrow & x = \frac{-221}{1827} & & \\ & V = \left\{ \frac{-221}{1827} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & -8x+\frac{3}{8} \\\Leftrightarrow & -28x-\frac{21}{8}& = & -8x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{-21} & = & \color{red}{-64x} +3 \\\Leftrightarrow & -224x \color{red}{-21} \color{blue}{+21} \color{blue}{+64x} & = & \color{red}{-64x} +3 \color{blue}{+64x} \color{blue}{+21} \\\Leftrightarrow & -224x+64x& = & 3+21 \\\Leftrightarrow & \color{red}{-160} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-160} & & \\\Leftrightarrow & x = \frac{-3}{20} & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{3})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{16}{3}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-112} & = & \color{red}{105x} +9 \\\Leftrightarrow & -252x \color{red}{-112} \color{blue}{+112} \color{blue}{-105x} & = & \color{red}{105x} +9 \color{blue}{-105x} \color{blue}{+112} \\\Leftrightarrow & -252x-105x& = & 9+112 \\\Leftrightarrow & \color{red}{-357} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-357} & & \\\Leftrightarrow & x = \frac{-121}{357} & & \\ & V = \left\{ \frac{-121}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{11})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{20}{11}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{140}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-140} & = & \color{red}{385x} +99 \\\Leftrightarrow & -924x \color{red}{-140} \color{blue}{+140} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{+140} \\\Leftrightarrow & -924x-385x& = & 99+140 \\\Leftrightarrow & \color{red}{-1309} x& = & 239 \\\Leftrightarrow & x = \frac{239}{-1309} & & \\\Leftrightarrow & x = \frac{-239}{1309} & & \\ & V = \left\{ \frac{-239}{1309} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-2)& = & -3x+\frac{4}{3} \\\Leftrightarrow & -14x+14& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x+ \frac{42}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{+42} & = & \color{red}{-9x} +4 \\\Leftrightarrow & -42x \color{red}{+42} \color{blue}{-42} \color{blue}{+9x} & = & \color{red}{-9x} +4 \color{blue}{+9x} \color{blue}{-42} \\\Leftrightarrow & -42x+9x& = & 4-42 \\\Leftrightarrow & \color{red}{-33} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-33} & & \\\Leftrightarrow & x = \frac{38}{33} & & \\ & V = \left\{ \frac{38}{33} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{11})& = & -3x+\frac{7}{10} \\\Leftrightarrow & 28x-\frac{21}{11}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3080}{ \color{blue}{110} }x- \frac{210}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3080x \color{red}{-210} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 3080x \color{red}{-210} \color{blue}{+210} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{+210} \\\Leftrightarrow & 3080x+330x& = & 77+210 \\\Leftrightarrow & \color{red}{3410} x& = & 287 \\\Leftrightarrow & x = \frac{287}{3410} & & \\ & V = \left\{ \frac{287}{3410} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{2})& = & 4x+\frac{3}{4} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 4x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{30}{ \color{blue}{4} })& = & (\frac{16}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-30} & = & \color{red}{16x} +3 \\\Leftrightarrow & -60x \color{red}{-30} \color{blue}{+30} \color{blue}{-16x} & = & \color{red}{16x} +3 \color{blue}{-16x} \color{blue}{+30} \\\Leftrightarrow & -60x-16x& = & 3+30 \\\Leftrightarrow & \color{red}{-76} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-76} & & \\\Leftrightarrow & x = \frac{-33}{76} & & \\ & V = \left\{ \frac{-33}{76} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{11})& = & 2x+\frac{10}{3} \\\Leftrightarrow & -25x-\frac{20}{11}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{60}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-60} & = & \color{red}{66x} +110 \\\Leftrightarrow & -825x \color{red}{-60} \color{blue}{+60} \color{blue}{-66x} & = & \color{red}{66x} +110 \color{blue}{-66x} \color{blue}{+60} \\\Leftrightarrow & -825x-66x& = & 110+60 \\\Leftrightarrow & \color{red}{-891} x& = & 170 \\\Leftrightarrow & x = \frac{170}{-891} & & \\\Leftrightarrow & x = \frac{-170}{891} & & \\ & V = \left\{ \frac{-170}{891} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-10} & = & \color{red}{77x} +6 \\\Leftrightarrow & 110x \color{red}{-10} \color{blue}{+10} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{+10} \\\Leftrightarrow & 110x-77x& = & 6+10 \\\Leftrightarrow & \color{red}{33} x& = & 16 \\\Leftrightarrow & x = \frac{16}{33} & & \\ & V = \left\{ \frac{16}{33} \right\} & \\\end{align}\)