Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{7})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 24x-\frac{24}{7}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1344}{ \color{blue}{56} }x- \frac{192}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1344x \color{red}{-192} & = & \color{red}{-392x} +35 \\\Leftrightarrow & 1344x \color{red}{-192} \color{blue}{+192} \color{blue}{+392x} & = & \color{red}{-392x} +35 \color{blue}{+392x} \color{blue}{+192} \\\Leftrightarrow & 1344x+392x& = & 35+192 \\\Leftrightarrow & \color{red}{1736} x& = & 227 \\\Leftrightarrow & x = \frac{227}{1736} & & \\ & V = \left\{ \frac{227}{1736} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{6}{11}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+30} & = & \color{red}{495x} +88 \\\Leftrightarrow & -440x \color{red}{+30} \color{blue}{-30} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{-30} \\\Leftrightarrow & -440x-495x& = & 88-30 \\\Leftrightarrow & \color{red}{-935} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-935} & & \\\Leftrightarrow & x = \frac{-58}{935} & & \\ & V = \left\{ \frac{-58}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 25x-\frac{10}{7}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-110} & = & \color{red}{154x} +42 \\\Leftrightarrow & 1925x \color{red}{-110} \color{blue}{+110} \color{blue}{-154x} & = & \color{red}{154x} +42 \color{blue}{-154x} \color{blue}{+110} \\\Leftrightarrow & 1925x-154x& = & 42+110 \\\Leftrightarrow & \color{red}{1771} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1771} & & \\ & V = \left\{ \frac{152}{1771} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{4})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 10x-\frac{15}{4}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{200}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 200x \color{red}{-75} & = & \color{red}{140x} +32 \\\Leftrightarrow & 200x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +32 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & 200x-140x& = & 32+75 \\\Leftrightarrow & \color{red}{60} x& = & 107 \\\Leftrightarrow & x = \frac{107}{60} & & \\ & V = \left\{ \frac{107}{60} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{16}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x- \frac{16}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{-16} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 80x \color{red}{-16} \color{blue}{+16} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+16} \\\Leftrightarrow & 80x+35x& = & 6+16 \\\Leftrightarrow & \color{red}{115} x& = & 22 \\\Leftrightarrow & x = \frac{22}{115} & & \\ & V = \left\{ \frac{22}{115} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{11})& = & 3x+\frac{7}{12} \\\Leftrightarrow & -20x-\frac{10}{11}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-2640}{ \color{blue}{132} }x- \frac{120}{ \color{blue}{132} })& = & (\frac{396}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -2640x \color{red}{-120} & = & \color{red}{396x} +77 \\\Leftrightarrow & -2640x \color{red}{-120} \color{blue}{+120} \color{blue}{-396x} & = & \color{red}{396x} +77 \color{blue}{-396x} \color{blue}{+120} \\\Leftrightarrow & -2640x-396x& = & 77+120 \\\Leftrightarrow & \color{red}{-3036} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-3036} & & \\\Leftrightarrow & x = \frac{-197}{3036} & & \\ & V = \left\{ \frac{-197}{3036} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1056}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1056x \color{red}{+72} & = & \color{red}{220x} +77 \\\Leftrightarrow & 1056x \color{red}{+72} \color{blue}{-72} \color{blue}{-220x} & = & \color{red}{220x} +77 \color{blue}{-220x} \color{blue}{-72} \\\Leftrightarrow & 1056x-220x& = & 77-72 \\\Leftrightarrow & \color{red}{836} x& = & 5 \\\Leftrightarrow & x = \frac{5}{836} & & \\ & V = \left\{ \frac{5}{836} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{4}{3})& = & -5x+\frac{3}{11} \\\Leftrightarrow & -14x-\frac{28}{3}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{-308} & = & \color{red}{-165x} +9 \\\Leftrightarrow & -462x \color{red}{-308} \color{blue}{+308} \color{blue}{+165x} & = & \color{red}{-165x} +9 \color{blue}{+165x} \color{blue}{+308} \\\Leftrightarrow & -462x+165x& = & 9+308 \\\Leftrightarrow & \color{red}{-297} x& = & 317 \\\Leftrightarrow & x = \frac{317}{-297} & & \\\Leftrightarrow & x = \frac{-317}{297} & & \\ & V = \left\{ \frac{-317}{297} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{8})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{21}{8}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{-63} & = & \color{red}{216x} +32 \\\Leftrightarrow & -672x \color{red}{-63} \color{blue}{+63} \color{blue}{-216x} & = & \color{red}{216x} +32 \color{blue}{-216x} \color{blue}{+63} \\\Leftrightarrow & -672x-216x& = & 32+63 \\\Leftrightarrow & \color{red}{-888} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-888} & & \\\Leftrightarrow & x = \frac{-95}{888} & & \\ & V = \left\{ \frac{-95}{888} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{11})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{-20} & = & \color{red}{198x} +77 \\\Leftrightarrow & 176x \color{red}{-20} \color{blue}{+20} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{+20} \\\Leftrightarrow & 176x-198x& = & 77+20 \\\Leftrightarrow & \color{red}{-22} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-22} & & \\\Leftrightarrow & x = \frac{-97}{22} & & \\ & V = \left\{ \frac{-97}{22} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{11})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 28x+\frac{14}{11}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{616}{ \color{blue}{22} }x+ \frac{28}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 616x \color{red}{+28} & = & \color{red}{198x} +55 \\\Leftrightarrow & 616x \color{red}{+28} \color{blue}{-28} \color{blue}{-198x} & = & \color{red}{198x} +55 \color{blue}{-198x} \color{blue}{-28} \\\Leftrightarrow & 616x-198x& = & 55-28 \\\Leftrightarrow & \color{red}{418} x& = & 27 \\\Leftrightarrow & x = \frac{27}{418} & & \\ & V = \left\{ \frac{27}{418} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 20x+\frac{16}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{+64} & = & \color{red}{196x} +63 \\\Leftrightarrow & 560x \color{red}{+64} \color{blue}{-64} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{-64} \\\Leftrightarrow & 560x-196x& = & 63-64 \\\Leftrightarrow & \color{red}{364} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{364} & & \\ & V = \left\{ \frac{-1}{364} \right\} & \\\end{align}\)