Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1344}{ \color{blue}{56} }x+ \frac{240}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1344x \color{red}{+240} & = & \color{red}{280x} +63 \\\Leftrightarrow & 1344x \color{red}{+240} \color{blue}{-240} \color{blue}{-280x} & = & \color{red}{280x} +63 \color{blue}{-280x} \color{blue}{-240} \\\Leftrightarrow & 1344x-280x& = & 63-240 \\\Leftrightarrow & \color{red}{1064} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{1064} & & \\ & V = \left\{ \frac{-177}{1064} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{2})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 14x-\frac{21}{2}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x- \frac{189}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{-189} & = & \color{red}{-162x} +8 \\\Leftrightarrow & 252x \color{red}{-189} \color{blue}{+189} \color{blue}{+162x} & = & \color{red}{-162x} +8 \color{blue}{+162x} \color{blue}{+189} \\\Leftrightarrow & 252x+162x& = & 8+189 \\\Leftrightarrow & \color{red}{414} x& = & 197 \\\Leftrightarrow & x = \frac{197}{414} & & \\ & V = \left\{ \frac{197}{414} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{4})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 21x-\frac{35}{4}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{105}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-105} & = & \color{red}{96x} +8 \\\Leftrightarrow & 252x \color{red}{-105} \color{blue}{+105} \color{blue}{-96x} & = & \color{red}{96x} +8 \color{blue}{-96x} \color{blue}{+105} \\\Leftrightarrow & 252x-96x& = & 8+105 \\\Leftrightarrow & \color{red}{156} x& = & 113 \\\Leftrightarrow & x = \frac{113}{156} & & \\ & V = \left\{ \frac{113}{156} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -6x+\frac{4}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+16} & = & \color{red}{196x} +35 \\\Leftrightarrow & -168x \color{red}{+16} \color{blue}{-16} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{-16} \\\Leftrightarrow & -168x-196x& = & 35-16 \\\Leftrightarrow & \color{red}{-364} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-364} & & \\\Leftrightarrow & x = \frac{-19}{364} & & \\ & V = \left\{ \frac{-19}{364} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -10x+\frac{15}{4}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+45} & = & \color{red}{84x} +10 \\\Leftrightarrow & -120x \color{red}{+45} \color{blue}{-45} \color{blue}{-84x} & = & \color{red}{84x} +10 \color{blue}{-84x} \color{blue}{-45} \\\Leftrightarrow & -120x-84x& = & 10-45 \\\Leftrightarrow & \color{red}{-204} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-204} & & \\\Leftrightarrow & x = \frac{35}{204} & & \\ & V = \left\{ \frac{35}{204} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 24x+\frac{12}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+36} & = & \color{red}{-165x} +110 \\\Leftrightarrow & 792x \color{red}{+36} \color{blue}{-36} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{-36} \\\Leftrightarrow & 792x+165x& = & 110-36 \\\Leftrightarrow & \color{red}{957} x& = & 74 \\\Leftrightarrow & x = \frac{74}{957} & & \\ & V = \left\{ \frac{74}{957} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{9})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{20}{9}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+20} & = & \color{red}{63x} +6 \\\Leftrightarrow & -144x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & -144x-63x& = & 6-20 \\\Leftrightarrow & \color{red}{-207} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-207} & & \\\Leftrightarrow & x = \frac{14}{207} & & \\ & V = \left\{ \frac{14}{207} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -4x-\frac{10}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-88}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -88x \color{red}{-20} & = & \color{red}{110x} +55 \\\Leftrightarrow & -88x \color{red}{-20} \color{blue}{+20} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{+20} \\\Leftrightarrow & -88x-110x& = & 55+20 \\\Leftrightarrow & \color{red}{-198} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-198} & & \\\Leftrightarrow & x = \frac{-25}{66} & & \\ & V = \left\{ \frac{-25}{66} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{2})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{15}{2}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+75} & = & \color{red}{-50x} +16 \\\Leftrightarrow & 120x \color{red}{+75} \color{blue}{-75} \color{blue}{+50x} & = & \color{red}{-50x} +16 \color{blue}{+50x} \color{blue}{-75} \\\Leftrightarrow & 120x+50x& = & 16-75 \\\Leftrightarrow & \color{red}{170} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{170} & & \\ & V = \left\{ \frac{-59}{170} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-18} & = & \color{red}{25x} +4 \\\Leftrightarrow & 90x \color{red}{-18} \color{blue}{+18} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{+18} \\\Leftrightarrow & 90x-25x& = & 4+18 \\\Leftrightarrow & \color{red}{65} x& = & 22 \\\Leftrightarrow & x = \frac{22}{65} & & \\ & V = \left\{ \frac{22}{65} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{3})& = & 9x+\frac{5}{3} \\\Leftrightarrow & 10x-\frac{8}{3}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{-8} & = & \color{red}{27x} +5 \\\Leftrightarrow & 30x \color{red}{-8} \color{blue}{+8} \color{blue}{-27x} & = & \color{red}{27x} +5 \color{blue}{-27x} \color{blue}{+8} \\\Leftrightarrow & 30x-27x& = & 5+8 \\\Leftrightarrow & \color{red}{3} x& = & 13 \\\Leftrightarrow & x = \frac{13}{3} & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+1)& = & -5x+\frac{3}{4} \\\Leftrightarrow & -28x-7& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-112}{ \color{blue}{4} }x- \frac{28}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -112x \color{red}{-28} & = & \color{red}{-20x} +3 \\\Leftrightarrow & -112x \color{red}{-28} \color{blue}{+28} \color{blue}{+20x} & = & \color{red}{-20x} +3 \color{blue}{+20x} \color{blue}{+28} \\\Leftrightarrow & -112x+20x& = & 3+28 \\\Leftrightarrow & \color{red}{-92} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-92} & & \\\Leftrightarrow & x = \frac{-31}{92} & & \\ & V = \left\{ \frac{-31}{92} \right\} & \\\end{align}\)