Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{11})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 10x+\frac{25}{11}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x+ \frac{50}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{+50} & = & \color{red}{-198x} +77 \\\Leftrightarrow & 220x \color{red}{+50} \color{blue}{-50} \color{blue}{+198x} & = & \color{red}{-198x} +77 \color{blue}{+198x} \color{blue}{-50} \\\Leftrightarrow & 220x+198x& = & 77-50 \\\Leftrightarrow & \color{red}{418} x& = & 27 \\\Leftrightarrow & x = \frac{27}{418} & & \\ & V = \left\{ \frac{27}{418} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & 6x+\frac{7}{8} \\\Leftrightarrow & -28x-\frac{21}{8}& = & 6x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{48}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{-21} & = & \color{red}{48x} +7 \\\Leftrightarrow & -224x \color{red}{-21} \color{blue}{+21} \color{blue}{-48x} & = & \color{red}{48x} +7 \color{blue}{-48x} \color{blue}{+21} \\\Leftrightarrow & -224x-48x& = & 7+21 \\\Leftrightarrow & \color{red}{-272} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-272} & & \\\Leftrightarrow & x = \frac{-7}{68} & & \\ & V = \left\{ \frac{-7}{68} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{5})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 14x-\frac{28}{5}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{-308} & = & \color{red}{-165x} +50 \\\Leftrightarrow & 770x \color{red}{-308} \color{blue}{+308} \color{blue}{+165x} & = & \color{red}{-165x} +50 \color{blue}{+165x} \color{blue}{+308} \\\Leftrightarrow & 770x+165x& = & 50+308 \\\Leftrightarrow & \color{red}{935} x& = & 358 \\\Leftrightarrow & x = \frac{358}{935} & & \\ & V = \left\{ \frac{358}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{175x} +10 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 420x-175x& = & 10-84 \\\Leftrightarrow & \color{red}{245} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{245} & & \\ & V = \left\{ \frac{-74}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-24} & = & \color{red}{55x} +6 \\\Leftrightarrow & -132x \color{red}{-24} \color{blue}{+24} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+24} \\\Leftrightarrow & -132x-55x& = & 6+24 \\\Leftrightarrow & \color{red}{-187} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-187} & & \\\Leftrightarrow & x = \frac{-30}{187} & & \\ & V = \left\{ \frac{-30}{187} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-16} & = & \color{red}{49x} +6 \\\Leftrightarrow & -112x \color{red}{-16} \color{blue}{+16} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+16} \\\Leftrightarrow & -112x-49x& = & 6+16 \\\Leftrightarrow & \color{red}{-161} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-161} & & \\\Leftrightarrow & x = \frac{-22}{161} & & \\ & V = \left\{ \frac{-22}{161} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+48} & = & \color{red}{-392x} +63 \\\Leftrightarrow & -560x \color{red}{+48} \color{blue}{-48} \color{blue}{+392x} & = & \color{red}{-392x} +63 \color{blue}{+392x} \color{blue}{-48} \\\Leftrightarrow & -560x+392x& = & 63-48 \\\Leftrightarrow & \color{red}{-168} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-168} & & \\\Leftrightarrow & x = \frac{-5}{56} & & \\ & V = \left\{ \frac{-5}{56} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 20x+\frac{16}{3}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{48}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+48} & = & \color{red}{-63x} +10 \\\Leftrightarrow & 180x \color{red}{+48} \color{blue}{-48} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{-48} \\\Leftrightarrow & 180x+63x& = & 10-48 \\\Leftrightarrow & \color{red}{243} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{243} & & \\ & V = \left\{ \frac{-38}{243} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{3}{11})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 20x+\frac{15}{11}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{30}{ \color{blue}{22} })& = & (\frac{-198}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+30} & = & \color{red}{-198x} +55 \\\Leftrightarrow & 440x \color{red}{+30} \color{blue}{-30} \color{blue}{+198x} & = & \color{red}{-198x} +55 \color{blue}{+198x} \color{blue}{-30} \\\Leftrightarrow & 440x+198x& = & 55-30 \\\Leftrightarrow & \color{red}{638} x& = & 25 \\\Leftrightarrow & x = \frac{25}{638} & & \\ & V = \left\{ \frac{25}{638} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{15}{8}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{96}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 96x \color{red}{-15} & = & \color{red}{40x} +12 \\\Leftrightarrow & 96x \color{red}{-15} \color{blue}{+15} \color{blue}{-40x} & = & \color{red}{40x} +12 \color{blue}{-40x} \color{blue}{+15} \\\Leftrightarrow & 96x-40x& = & 12+15 \\\Leftrightarrow & \color{red}{56} x& = & 27 \\\Leftrightarrow & x = \frac{27}{56} & & \\ & V = \left\{ \frac{27}{56} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-36} & = & \color{red}{105x} +50 \\\Leftrightarrow & -90x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -90x-105x& = & 50+36 \\\Leftrightarrow & \color{red}{-195} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-195} & & \\\Leftrightarrow & x = \frac{-86}{195} & & \\ & V = \left\{ \frac{-86}{195} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-154} & = & \color{red}{297x} +12 \\\Leftrightarrow & 924x \color{red}{-154} \color{blue}{+154} \color{blue}{-297x} & = & \color{red}{297x} +12 \color{blue}{-297x} \color{blue}{+154} \\\Leftrightarrow & 924x-297x& = & 12+154 \\\Leftrightarrow & \color{red}{627} x& = & 166 \\\Leftrightarrow & x = \frac{166}{627} & & \\ & V = \left\{ \frac{166}{627} \right\} & \\\end{align}\)