Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{3})& = & -8x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{10}{3}& = & -8x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{+110} & = & \color{red}{-264x} +21 \\\Leftrightarrow & -495x \color{red}{+110} \color{blue}{-110} \color{blue}{+264x} & = & \color{red}{-264x} +21 \color{blue}{+264x} \color{blue}{-110} \\\Leftrightarrow & -495x+264x& = & 21-110 \\\Leftrightarrow & \color{red}{-231} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-231} & & \\\Leftrightarrow & x = \frac{89}{231} & & \\ & V = \left\{ \frac{89}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & 3x+\frac{10}{11} \\\Leftrightarrow & -14x+\frac{14}{5}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{+154} & = & \color{red}{165x} +50 \\\Leftrightarrow & -770x \color{red}{+154} \color{blue}{-154} \color{blue}{-165x} & = & \color{red}{165x} +50 \color{blue}{-165x} \color{blue}{-154} \\\Leftrightarrow & -770x-165x& = & 50-154 \\\Leftrightarrow & \color{red}{-935} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-935} & & \\\Leftrightarrow & x = \frac{104}{935} & & \\ & V = \left\{ \frac{104}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & 8x+\frac{8}{11} \\\Leftrightarrow & -21x+\frac{21}{8}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{+231} & = & \color{red}{704x} +64 \\\Leftrightarrow & -1848x \color{red}{+231} \color{blue}{-231} \color{blue}{-704x} & = & \color{red}{704x} +64 \color{blue}{-704x} \color{blue}{-231} \\\Leftrightarrow & -1848x-704x& = & 64-231 \\\Leftrightarrow & \color{red}{-2552} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{-2552} & & \\\Leftrightarrow & x = \frac{167}{2552} & & \\ & V = \left\{ \frac{167}{2552} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{20}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-60} & = & \color{red}{147x} +14 \\\Leftrightarrow & 315x \color{red}{-60} \color{blue}{+60} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+60} \\\Leftrightarrow & 315x-147x& = & 14+60 \\\Leftrightarrow & \color{red}{168} x& = & 74 \\\Leftrightarrow & x = \frac{74}{168} & & \\\Leftrightarrow & x = \frac{37}{84} & & \\ & V = \left\{ \frac{37}{84} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{4}{5}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{+36} & = & \color{red}{135x} +20 \\\Leftrightarrow & 450x \color{red}{+36} \color{blue}{-36} \color{blue}{-135x} & = & \color{red}{135x} +20 \color{blue}{-135x} \color{blue}{-36} \\\Leftrightarrow & 450x-135x& = & 20-36 \\\Leftrightarrow & \color{red}{315} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{315} & & \\ & V = \left\{ \frac{-16}{315} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{3})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -10x-\frac{20}{3}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-100} & = & \color{red}{-105x} +6 \\\Leftrightarrow & -150x \color{red}{-100} \color{blue}{+100} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{+100} \\\Leftrightarrow & -150x+105x& = & 6+100 \\\Leftrightarrow & \color{red}{-45} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-45} & & \\\Leftrightarrow & x = \frac{-106}{45} & & \\ & V = \left\{ \frac{-106}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{4})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -14x+\frac{35}{4}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-616}{ \color{blue}{44} }x+ \frac{385}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -616x \color{red}{+385} & = & \color{red}{-132x} +40 \\\Leftrightarrow & -616x \color{red}{+385} \color{blue}{-385} \color{blue}{+132x} & = & \color{red}{-132x} +40 \color{blue}{+132x} \color{blue}{-385} \\\Leftrightarrow & -616x+132x& = & 40-385 \\\Leftrightarrow & \color{red}{-484} x& = & -345 \\\Leftrightarrow & x = \frac{-345}{-484} & & \\\Leftrightarrow & x = \frac{345}{484} & & \\ & V = \left\{ \frac{345}{484} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{10}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-110} & = & \color{red}{539x} +35 \\\Leftrightarrow & -462x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & -462x-539x& = & 35+110 \\\Leftrightarrow & \color{red}{-1001} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-1001} & & \\\Leftrightarrow & x = \frac{-145}{1001} & & \\ & V = \left\{ \frac{-145}{1001} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{12}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-12} & = & \color{red}{-99x} +6 \\\Leftrightarrow & 88x \color{red}{-12} \color{blue}{+12} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{+12} \\\Leftrightarrow & 88x+99x& = & 6+12 \\\Leftrightarrow & \color{red}{187} x& = & 18 \\\Leftrightarrow & x = \frac{18}{187} & & \\ & V = \left\{ \frac{18}{187} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{10})& = & -5x+\frac{7}{4} \\\Leftrightarrow & 9x+\frac{9}{10}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{+18} & = & \color{red}{-100x} +35 \\\Leftrightarrow & 180x \color{red}{+18} \color{blue}{-18} \color{blue}{+100x} & = & \color{red}{-100x} +35 \color{blue}{+100x} \color{blue}{-18} \\\Leftrightarrow & 180x+100x& = & 35-18 \\\Leftrightarrow & \color{red}{280} x& = & 17 \\\Leftrightarrow & x = \frac{17}{280} & & \\ & V = \left\{ \frac{17}{280} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{11})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -6x-\frac{8}{11}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-40} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -330x \color{red}{-40} \color{blue}{+40} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+40} \\\Leftrightarrow & -330x+385x& = & 33+40 \\\Leftrightarrow & \color{red}{55} x& = & 73 \\\Leftrightarrow & x = \frac{73}{55} & & \\ & V = \left\{ \frac{73}{55} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{9})& = & 9x+\frac{3}{5} \\\Leftrightarrow & -8x+\frac{4}{9}& = & 9x+\frac{3}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{27}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+20} & = & \color{red}{405x} +27 \\\Leftrightarrow & -360x \color{red}{+20} \color{blue}{-20} \color{blue}{-405x} & = & \color{red}{405x} +27 \color{blue}{-405x} \color{blue}{-20} \\\Leftrightarrow & -360x-405x& = & 27-20 \\\Leftrightarrow & \color{red}{-765} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-765} & & \\\Leftrightarrow & x = \frac{-7}{765} & & \\ & V = \left\{ \frac{-7}{765} \right\} & \\\end{align}\)