Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{4})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 14x-\frac{35}{4}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{504}{ \color{blue}{36} }x- \frac{315}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{20}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 504x \color{red}{-315} & = & \color{red}{-180x} +20 \\\Leftrightarrow & 504x \color{red}{-315} \color{blue}{+315} \color{blue}{+180x} & = & \color{red}{-180x} +20 \color{blue}{+180x} \color{blue}{+315} \\\Leftrightarrow & 504x+180x& = & 20+315 \\\Leftrightarrow & \color{red}{684} x& = & 335 \\\Leftrightarrow & x = \frac{335}{684} & & \\ & V = \left\{ \frac{335}{684} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{5})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{8}{5}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-88} & = & \color{red}{495x} +30 \\\Leftrightarrow & -440x \color{red}{-88} \color{blue}{+88} \color{blue}{-495x} & = & \color{red}{495x} +30 \color{blue}{-495x} \color{blue}{+88} \\\Leftrightarrow & -440x-495x& = & 30+88 \\\Leftrightarrow & \color{red}{-935} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-935} & & \\\Leftrightarrow & x = \frac{-118}{935} & & \\ & V = \left\{ \frac{-118}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-140} & = & \color{red}{63x} +6 \\\Leftrightarrow & 168x \color{red}{-140} \color{blue}{+140} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{+140} \\\Leftrightarrow & 168x-63x& = & 6+140 \\\Leftrightarrow & \color{red}{105} x& = & 146 \\\Leftrightarrow & x = \frac{146}{105} & & \\ & V = \left\{ \frac{146}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+24} & = & \color{red}{-55x} +10 \\\Leftrightarrow & 132x \color{red}{+24} \color{blue}{-24} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{-24} \\\Leftrightarrow & 132x+55x& = & 10-24 \\\Leftrightarrow & \color{red}{187} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{187} & & \\ & V = \left\{ \frac{-14}{187} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+20} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -280x \color{red}{+20} \color{blue}{-20} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{-20} \\\Leftrightarrow & -280x+98x& = & 35-20 \\\Leftrightarrow & \color{red}{-182} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-182} & & \\\Leftrightarrow & x = \frac{-15}{182} & & \\ & V = \left\{ \frac{-15}{182} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{7})& = & -4x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{20}{7}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+60} & = & \color{red}{-84x} +14 \\\Leftrightarrow & -315x \color{red}{+60} \color{blue}{-60} \color{blue}{+84x} & = & \color{red}{-84x} +14 \color{blue}{+84x} \color{blue}{-60} \\\Leftrightarrow & -315x+84x& = & 14-60 \\\Leftrightarrow & \color{red}{-231} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-231} & & \\\Leftrightarrow & x = \frac{46}{231} & & \\ & V = \left\{ \frac{46}{231} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{11})& = & -9x+\frac{4}{11} \\\Leftrightarrow & -4x-\frac{4}{11}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x- \frac{4}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{-4} & = & \color{red}{-99x} +4 \\\Leftrightarrow & -44x \color{red}{-4} \color{blue}{+4} \color{blue}{+99x} & = & \color{red}{-99x} +4 \color{blue}{+99x} \color{blue}{+4} \\\Leftrightarrow & -44x+99x& = & 4+4 \\\Leftrightarrow & \color{red}{55} x& = & 8 \\\Leftrightarrow & x = \frac{8}{55} & & \\ & V = \left\{ \frac{8}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -10x+\frac{4}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-12} \\\Leftrightarrow & -150x+105x& = & 40-12 \\\Leftrightarrow & \color{red}{-45} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-45} & & \\\Leftrightarrow & x = \frac{-28}{45} & & \\ & V = \left\{ \frac{-28}{45} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{+100} & = & \color{red}{490x} +21 \\\Leftrightarrow & -420x \color{red}{+100} \color{blue}{-100} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{-100} \\\Leftrightarrow & -420x-490x& = & 21-100 \\\Leftrightarrow & \color{red}{-910} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-910} & & \\\Leftrightarrow & x = \frac{79}{910} & & \\ & V = \left\{ \frac{79}{910} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 14x+\frac{14}{5}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{+154} & = & \color{red}{165x} +50 \\\Leftrightarrow & 770x \color{red}{+154} \color{blue}{-154} \color{blue}{-165x} & = & \color{red}{165x} +50 \color{blue}{-165x} \color{blue}{-154} \\\Leftrightarrow & 770x-165x& = & 50-154 \\\Leftrightarrow & \color{red}{605} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{605} & & \\ & V = \left\{ \frac{-104}{605} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{3})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 20x-\frac{10}{3}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{30}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-30} & = & \color{red}{63x} +8 \\\Leftrightarrow & 180x \color{red}{-30} \color{blue}{+30} \color{blue}{-63x} & = & \color{red}{63x} +8 \color{blue}{-63x} \color{blue}{+30} \\\Leftrightarrow & 180x-63x& = & 8+30 \\\Leftrightarrow & \color{red}{117} x& = & 38 \\\Leftrightarrow & x = \frac{38}{117} & & \\ & V = \left\{ \frac{38}{117} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{9})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -14x+\frac{28}{9}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-630}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -630x \color{red}{+140} & = & \color{red}{-225x} +72 \\\Leftrightarrow & -630x \color{red}{+140} \color{blue}{-140} \color{blue}{+225x} & = & \color{red}{-225x} +72 \color{blue}{+225x} \color{blue}{-140} \\\Leftrightarrow & -630x+225x& = & 72-140 \\\Leftrightarrow & \color{red}{-405} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-405} & & \\\Leftrightarrow & x = \frac{68}{405} & & \\ & V = \left\{ \frac{68}{405} \right\} & \\\end{align}\)