Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{8})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -9x+\frac{15}{8}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-72}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{10}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -72x \color{red}{+15} & = & \color{red}{40x} +10 \\\Leftrightarrow & -72x \color{red}{+15} \color{blue}{-15} \color{blue}{-40x} & = & \color{red}{40x} +10 \color{blue}{-40x} \color{blue}{-15} \\\Leftrightarrow & -72x-40x& = & 10-15 \\\Leftrightarrow & \color{red}{-112} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-112} & & \\\Leftrightarrow & x = \frac{5}{112} & & \\ & V = \left\{ \frac{5}{112} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{4})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -14x-\frac{35}{4}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-280}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -280x \color{red}{-175} & = & \color{red}{-60x} +16 \\\Leftrightarrow & -280x \color{red}{-175} \color{blue}{+175} \color{blue}{+60x} & = & \color{red}{-60x} +16 \color{blue}{+60x} \color{blue}{+175} \\\Leftrightarrow & -280x+60x& = & 16+175 \\\Leftrightarrow & \color{red}{-220} x& = & 191 \\\Leftrightarrow & x = \frac{191}{-220} & & \\\Leftrightarrow & x = \frac{-191}{220} & & \\ & V = \left\{ \frac{-191}{220} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{4}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+20} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -90x \color{red}{+20} \color{blue}{-20} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-20} \\\Leftrightarrow & -90x+105x& = & 18-20 \\\Leftrightarrow & \color{red}{15} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-30} & = & \color{red}{231x} +110 \\\Leftrightarrow & 660x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & 660x-231x& = & 110+30 \\\Leftrightarrow & \color{red}{429} x& = & 140 \\\Leftrightarrow & x = \frac{140}{429} & & \\ & V = \left\{ \frac{140}{429} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-40}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -40x \color{red}{+8} & = & \color{red}{-50x} +3 \\\Leftrightarrow & -40x \color{red}{+8} \color{blue}{-8} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{-8} \\\Leftrightarrow & -40x+50x& = & 3-8 \\\Leftrightarrow & \color{red}{10} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{10} & & \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & -9x+\frac{7}{10} \\\Leftrightarrow & 20x+\frac{10}{11}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2200}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2200x \color{red}{+100} & = & \color{red}{-990x} +77 \\\Leftrightarrow & 2200x \color{red}{+100} \color{blue}{-100} \color{blue}{+990x} & = & \color{red}{-990x} +77 \color{blue}{+990x} \color{blue}{-100} \\\Leftrightarrow & 2200x+990x& = & 77-100 \\\Leftrightarrow & \color{red}{3190} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{3190} & & \\ & V = \left\{ \frac{-23}{3190} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{8})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -14x-\frac{35}{8}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{385}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-385} & = & \color{red}{-440x} +80 \\\Leftrightarrow & -1232x \color{red}{-385} \color{blue}{+385} \color{blue}{+440x} & = & \color{red}{-440x} +80 \color{blue}{+440x} \color{blue}{+385} \\\Leftrightarrow & -1232x+440x& = & 80+385 \\\Leftrightarrow & \color{red}{-792} x& = & 465 \\\Leftrightarrow & x = \frac{465}{-792} & & \\\Leftrightarrow & x = \frac{-155}{264} & & \\ & V = \left\{ \frac{-155}{264} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{3})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{147x} +30 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{-147x} & = & \color{red}{147x} +30 \color{blue}{-147x} \color{blue}{-140} \\\Leftrightarrow & -420x-147x& = & 30-140 \\\Leftrightarrow & \color{red}{-567} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{-567} & & \\\Leftrightarrow & x = \frac{110}{567} & & \\ & V = \left\{ \frac{110}{567} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-90} & = & \color{red}{275x} +66 \\\Leftrightarrow & -660x \color{red}{-90} \color{blue}{+90} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+90} \\\Leftrightarrow & -660x-275x& = & 66+90 \\\Leftrightarrow & \color{red}{-935} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-935} & & \\\Leftrightarrow & x = \frac{-156}{935} & & \\ & V = \left\{ \frac{-156}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{11})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -6x-\frac{10}{11}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{-10} & = & \color{red}{77x} +3 \\\Leftrightarrow & -66x \color{red}{-10} \color{blue}{+10} \color{blue}{-77x} & = & \color{red}{77x} +3 \color{blue}{-77x} \color{blue}{+10} \\\Leftrightarrow & -66x-77x& = & 3+10 \\\Leftrightarrow & \color{red}{-143} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-143} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-150} & = & \color{red}{245x} +42 \\\Leftrightarrow & 1050x \color{red}{-150} \color{blue}{+150} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{+150} \\\Leftrightarrow & 1050x-245x& = & 42+150 \\\Leftrightarrow & \color{red}{805} x& = & 192 \\\Leftrightarrow & x = \frac{192}{805} & & \\ & V = \left\{ \frac{192}{805} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{2})& = & 8x+\frac{9}{4} \\\Leftrightarrow & -21x-\frac{21}{2}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-84}{ \color{blue}{4} }x- \frac{42}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -84x \color{red}{-42} & = & \color{red}{32x} +9 \\\Leftrightarrow & -84x \color{red}{-42} \color{blue}{+42} \color{blue}{-32x} & = & \color{red}{32x} +9 \color{blue}{-32x} \color{blue}{+42} \\\Leftrightarrow & -84x-32x& = & 9+42 \\\Leftrightarrow & \color{red}{-116} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-116} & & \\\Leftrightarrow & x = \frac{-51}{116} & & \\ & V = \left\{ \frac{-51}{116} \right\} & \\\end{align}\)