Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-40} & = & \color{red}{132x} +33 \\\Leftrightarrow & 440x \color{red}{-40} \color{blue}{+40} \color{blue}{-132x} & = & \color{red}{132x} +33 \color{blue}{-132x} \color{blue}{+40} \\\Leftrightarrow & 440x-132x& = & 33+40 \\\Leftrightarrow & \color{red}{308} x& = & 73 \\\Leftrightarrow & x = \frac{73}{308} & & \\ & V = \left\{ \frac{73}{308} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{7})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{12}{7}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-60} & = & \color{red}{315x} +28 \\\Leftrightarrow & -700x \color{red}{-60} \color{blue}{+60} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{+60} \\\Leftrightarrow & -700x-315x& = & 28+60 \\\Leftrightarrow & \color{red}{-1015} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-1015} & & \\\Leftrightarrow & x = \frac{-88}{1015} & & \\ & V = \left\{ \frac{-88}{1015} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{2})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 15x-\frac{25}{2}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{100}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-100} & = & \color{red}{-56x} +5 \\\Leftrightarrow & 120x \color{red}{-100} \color{blue}{+100} \color{blue}{+56x} & = & \color{red}{-56x} +5 \color{blue}{+56x} \color{blue}{+100} \\\Leftrightarrow & 120x+56x& = & 5+100 \\\Leftrightarrow & \color{red}{176} x& = & 105 \\\Leftrightarrow & x = \frac{105}{176} & & \\ & V = \left\{ \frac{105}{176} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{9})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 10x-\frac{8}{9}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-88} & = & \color{red}{-891x} +45 \\\Leftrightarrow & 990x \color{red}{-88} \color{blue}{+88} \color{blue}{+891x} & = & \color{red}{-891x} +45 \color{blue}{+891x} \color{blue}{+88} \\\Leftrightarrow & 990x+891x& = & 45+88 \\\Leftrightarrow & \color{red}{1881} x& = & 133 \\\Leftrightarrow & x = \frac{133}{1881} & & \\\Leftrightarrow & x = \frac{7}{99} & & \\ & V = \left\{ \frac{7}{99} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -10x+\frac{15}{2}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{+165} & = & \color{red}{154x} +8 \\\Leftrightarrow & -220x \color{red}{+165} \color{blue}{-165} \color{blue}{-154x} & = & \color{red}{154x} +8 \color{blue}{-154x} \color{blue}{-165} \\\Leftrightarrow & -220x-154x& = & 8-165 \\\Leftrightarrow & \color{red}{-374} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-374} & & \\\Leftrightarrow & x = \frac{157}{374} & & \\ & V = \left\{ \frac{157}{374} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-176} & = & \color{red}{-539x} +14 \\\Leftrightarrow & -1540x \color{red}{-176} \color{blue}{+176} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{+176} \\\Leftrightarrow & -1540x+539x& = & 14+176 \\\Leftrightarrow & \color{red}{-1001} x& = & 190 \\\Leftrightarrow & x = \frac{190}{-1001} & & \\\Leftrightarrow & x = \frac{-190}{1001} & & \\ & V = \left\{ \frac{-190}{1001} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{+80} & = & \color{red}{-245x} +49 \\\Leftrightarrow & 560x \color{red}{+80} \color{blue}{-80} \color{blue}{+245x} & = & \color{red}{-245x} +49 \color{blue}{+245x} \color{blue}{-80} \\\Leftrightarrow & 560x+245x& = & 49-80 \\\Leftrightarrow & \color{red}{805} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{805} & & \\ & V = \left\{ \frac{-31}{805} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{2})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 14x-\frac{21}{2}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{56}{ \color{blue}{4} }x- \frac{42}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 56x \color{red}{-42} & = & \color{red}{12x} +3 \\\Leftrightarrow & 56x \color{red}{-42} \color{blue}{+42} \color{blue}{-12x} & = & \color{red}{12x} +3 \color{blue}{-12x} \color{blue}{+42} \\\Leftrightarrow & 56x-12x& = & 3+42 \\\Leftrightarrow & \color{red}{44} x& = & 45 \\\Leftrightarrow & x = \frac{45}{44} & & \\ & V = \left\{ \frac{45}{44} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{9}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+27} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 90x \color{red}{+27} \color{blue}{-27} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-27} \\\Leftrightarrow & 90x+75x& = & 50-27 \\\Leftrightarrow & \color{red}{165} x& = & 23 \\\Leftrightarrow & x = \frac{23}{165} & & \\ & V = \left\{ \frac{23}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{9})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 28x-\frac{14}{9}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x- \frac{112}{ \color{blue}{72} })& = & (\frac{360}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{-112} & = & \color{red}{360x} +45 \\\Leftrightarrow & 2016x \color{red}{-112} \color{blue}{+112} \color{blue}{-360x} & = & \color{red}{360x} +45 \color{blue}{-360x} \color{blue}{+112} \\\Leftrightarrow & 2016x-360x& = & 45+112 \\\Leftrightarrow & \color{red}{1656} x& = & 157 \\\Leftrightarrow & x = \frac{157}{1656} & & \\ & V = \left\{ \frac{157}{1656} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{25}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{660}{ \color{blue}{66} }x+ \frac{150}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 660x \color{red}{+150} & = & \color{red}{-462x} +55 \\\Leftrightarrow & 660x \color{red}{+150} \color{blue}{-150} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{-150} \\\Leftrightarrow & 660x+462x& = & 55-150 \\\Leftrightarrow & \color{red}{1122} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{1122} & & \\ & V = \left\{ \frac{-95}{1122} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{3})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 4x+\frac{8}{3}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+56} & = & \color{red}{105x} +30 \\\Leftrightarrow & 84x \color{red}{+56} \color{blue}{-56} \color{blue}{-105x} & = & \color{red}{105x} +30 \color{blue}{-105x} \color{blue}{-56} \\\Leftrightarrow & 84x-105x& = & 30-56 \\\Leftrightarrow & \color{red}{-21} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-21} & & \\\Leftrightarrow & x = \frac{26}{21} & & \\ & V = \left\{ \frac{26}{21} \right\} & \\\end{align}\)