Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 4x-\frac{10}{7}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{112}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 112x \color{red}{-40} & = & \color{red}{-84x} +21 \\\Leftrightarrow & 112x \color{red}{-40} \color{blue}{+40} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{+40} \\\Leftrightarrow & 112x+84x& = & 21+40 \\\Leftrightarrow & \color{red}{196} x& = & 61 \\\Leftrightarrow & x = \frac{61}{196} & & \\ & V = \left\{ \frac{61}{196} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{11})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 9x-\frac{12}{11}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{-12} & = & \color{red}{-22x} +8 \\\Leftrightarrow & 99x \color{red}{-12} \color{blue}{+12} \color{blue}{+22x} & = & \color{red}{-22x} +8 \color{blue}{+22x} \color{blue}{+12} \\\Leftrightarrow & 99x+22x& = & 8+12 \\\Leftrightarrow & \color{red}{121} x& = & 20 \\\Leftrightarrow & x = \frac{20}{121} & & \\ & V = \left\{ \frac{20}{121} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{35}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{-175} & = & \color{red}{-75x} +18 \\\Leftrightarrow & 315x \color{red}{-175} \color{blue}{+175} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{+175} \\\Leftrightarrow & 315x+75x& = & 18+175 \\\Leftrightarrow & \color{red}{390} x& = & 193 \\\Leftrightarrow & x = \frac{193}{390} & & \\ & V = \left\{ \frac{193}{390} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & -6x+\frac{9}{7} \\\Leftrightarrow & 25x-\frac{10}{7}& = & -6x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-42}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-10} & = & \color{red}{-42x} +9 \\\Leftrightarrow & 175x \color{red}{-10} \color{blue}{+10} \color{blue}{+42x} & = & \color{red}{-42x} +9 \color{blue}{+42x} \color{blue}{+10} \\\Leftrightarrow & 175x+42x& = & 9+10 \\\Leftrightarrow & \color{red}{217} x& = & 19 \\\Leftrightarrow & x = \frac{19}{217} & & \\ & V = \left\{ \frac{19}{217} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+72} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 528x \color{red}{+72} \color{blue}{-72} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-72} \\\Leftrightarrow & 528x+220x& = & 33-72 \\\Leftrightarrow & \color{red}{748} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{748} & & \\ & V = \left\{ \frac{-39}{748} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{9})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x+\frac{35}{9}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+35} & = & \color{red}{-72x} +24 \\\Leftrightarrow & -189x \color{red}{+35} \color{blue}{-35} \color{blue}{+72x} & = & \color{red}{-72x} +24 \color{blue}{+72x} \color{blue}{-35} \\\Leftrightarrow & -189x+72x& = & 24-35 \\\Leftrightarrow & \color{red}{-117} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-117} & & \\\Leftrightarrow & x = \frac{11}{117} & & \\ & V = \left\{ \frac{11}{117} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{35x} +2 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & 168x-35x& = & 2-30 \\\Leftrightarrow & \color{red}{133} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{133} & & \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -1650x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{-1265} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-1265} & & \\\Leftrightarrow & x = \frac{-162}{1265} & & \\ & V = \left\{ \frac{-162}{1265} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{7})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{693x} +70 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{-693x} & = & \color{red}{693x} +70 \color{blue}{-693x} \color{blue}{-66} \\\Leftrightarrow & 616x-693x& = & 70-66 \\\Leftrightarrow & \color{red}{-77} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-77} & & \\\Leftrightarrow & x = \frac{-4}{77} & & \\ & V = \left\{ \frac{-4}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +2 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +2 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 2-12 \\\Leftrightarrow & \color{red}{-85} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-85} & & \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{12}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+60} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -880x \color{red}{+60} \color{blue}{-60} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-60} \\\Leftrightarrow & -880x+385x& = & 66-60 \\\Leftrightarrow & \color{red}{-495} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-495} & & \\\Leftrightarrow & x = \frac{-2}{165} & & \\ & V = \left\{ \frac{-2}{165} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -5x+\frac{3}{8} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-720}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -720x \color{red}{-96} & = & \color{red}{-200x} +15 \\\Leftrightarrow & -720x \color{red}{-96} \color{blue}{+96} \color{blue}{+200x} & = & \color{red}{-200x} +15 \color{blue}{+200x} \color{blue}{+96} \\\Leftrightarrow & -720x+200x& = & 15+96 \\\Leftrightarrow & \color{red}{-520} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-520} & & \\\Leftrightarrow & x = \frac{-111}{520} & & \\ & V = \left\{ \frac{-111}{520} \right\} & \\\end{align}\)