Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{5})& = & -9x+\frac{8}{11} \\\Leftrightarrow & 14x-\frac{28}{5}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{-308} & = & \color{red}{-495x} +40 \\\Leftrightarrow & 770x \color{red}{-308} \color{blue}{+308} \color{blue}{+495x} & = & \color{red}{-495x} +40 \color{blue}{+495x} \color{blue}{+308} \\\Leftrightarrow & 770x+495x& = & 40+308 \\\Leftrightarrow & \color{red}{1265} x& = & 348 \\\Leftrightarrow & x = \frac{348}{1265} & & \\ & V = \left\{ \frac{348}{1265} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{9})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{4}{9}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{720}{ \color{blue}{72} }x- \frac{32}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 720x \color{red}{-32} & = & \color{red}{504x} +63 \\\Leftrightarrow & 720x \color{red}{-32} \color{blue}{+32} \color{blue}{-504x} & = & \color{red}{504x} +63 \color{blue}{-504x} \color{blue}{+32} \\\Leftrightarrow & 720x-504x& = & 63+32 \\\Leftrightarrow & \color{red}{216} x& = & 95 \\\Leftrightarrow & x = \frac{95}{216} & & \\ & V = \left\{ \frac{95}{216} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -14x+\frac{14}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{+154} & = & \color{red}{275x} +50 \\\Leftrightarrow & -770x \color{red}{+154} \color{blue}{-154} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-154} \\\Leftrightarrow & -770x-275x& = & 50-154 \\\Leftrightarrow & \color{red}{-1045} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-1045} & & \\\Leftrightarrow & x = \frac{104}{1045} & & \\ & V = \left\{ \frac{104}{1045} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{+108} & = & \color{red}{-225x} +25 \\\Leftrightarrow & 810x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +25 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & 810x+225x& = & 25-108 \\\Leftrightarrow & \color{red}{1035} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{1035} & & \\ & V = \left\{ \frac{-83}{1035} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{11})& = & -4x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{10}{11}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-50} & = & \color{red}{-220x} +66 \\\Leftrightarrow & 825x \color{red}{-50} \color{blue}{+50} \color{blue}{+220x} & = & \color{red}{-220x} +66 \color{blue}{+220x} \color{blue}{+50} \\\Leftrightarrow & 825x+220x& = & 66+50 \\\Leftrightarrow & \color{red}{1045} x& = & 116 \\\Leftrightarrow & x = \frac{116}{1045} & & \\ & V = \left\{ \frac{116}{1045} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{11})& = & 3x+\frac{10}{11} \\\Leftrightarrow & -20x-\frac{12}{11}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-12} & = & \color{red}{33x} +10 \\\Leftrightarrow & -220x \color{red}{-12} \color{blue}{+12} \color{blue}{-33x} & = & \color{red}{33x} +10 \color{blue}{-33x} \color{blue}{+12} \\\Leftrightarrow & -220x-33x& = & 10+12 \\\Leftrightarrow & \color{red}{-253} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-253} & & \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & -8x+\frac{10}{7} \\\Leftrightarrow & -21x+\frac{21}{8}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1176}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1176x \color{red}{+147} & = & \color{red}{-448x} +80 \\\Leftrightarrow & -1176x \color{red}{+147} \color{blue}{-147} \color{blue}{+448x} & = & \color{red}{-448x} +80 \color{blue}{+448x} \color{blue}{-147} \\\Leftrightarrow & -1176x+448x& = & 80-147 \\\Leftrightarrow & \color{red}{-728} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-728} & & \\\Leftrightarrow & x = \frac{67}{728} & & \\ & V = \left\{ \frac{67}{728} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 24x \color{red}{-15} & = & \color{red}{-20x} +9 \\\Leftrightarrow & 24x \color{red}{-15} \color{blue}{+15} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{+15} \\\Leftrightarrow & 24x+20x& = & 9+15 \\\Leftrightarrow & \color{red}{44} x& = & 24 \\\Leftrightarrow & x = \frac{24}{44} & & \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{9})& = & 8x+\frac{4}{3} \\\Leftrightarrow & 35x+\frac{35}{9}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+35} & = & \color{red}{72x} +12 \\\Leftrightarrow & 315x \color{red}{+35} \color{blue}{-35} \color{blue}{-72x} & = & \color{red}{72x} +12 \color{blue}{-72x} \color{blue}{-35} \\\Leftrightarrow & 315x-72x& = & 12-35 \\\Leftrightarrow & \color{red}{243} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{243} & & \\ & V = \left\{ \frac{-23}{243} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+10} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -175x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -175x+49x& = & 10-10 \\\Leftrightarrow & \color{red}{-126} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-126} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{9})& = & 8x+\frac{5}{6} \\\Leftrightarrow & -21x+\frac{28}{9}& = & 8x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-378}{ \color{blue}{18} }x+ \frac{56}{ \color{blue}{18} })& = & (\frac{144}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -378x \color{red}{+56} & = & \color{red}{144x} +15 \\\Leftrightarrow & -378x \color{red}{+56} \color{blue}{-56} \color{blue}{-144x} & = & \color{red}{144x} +15 \color{blue}{-144x} \color{blue}{-56} \\\Leftrightarrow & -378x-144x& = & 15-56 \\\Leftrightarrow & \color{red}{-522} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-522} & & \\\Leftrightarrow & x = \frac{41}{522} & & \\ & V = \left\{ \frac{41}{522} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 9x+\frac{10}{9} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+108} & = & \color{red}{405x} +50 \\\Leftrightarrow & 900x \color{red}{+108} \color{blue}{-108} \color{blue}{-405x} & = & \color{red}{405x} +50 \color{blue}{-405x} \color{blue}{-108} \\\Leftrightarrow & 900x-405x& = & 50-108 \\\Leftrightarrow & \color{red}{495} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{495} & & \\ & V = \left\{ \frac{-58}{495} \right\} & \\\end{align}\)