Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{30}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+210} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -924x \color{red}{+210} \color{blue}{-210} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{-210} \\\Leftrightarrow & -924x+385x& = & 33-210 \\\Leftrightarrow & \color{red}{-539} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{-539} & & \\\Leftrightarrow & x = \frac{177}{539} & & \\ & V = \left\{ \frac{177}{539} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{11})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+126} & = & \color{red}{308x} +110 \\\Leftrightarrow & -1386x \color{red}{+126} \color{blue}{-126} \color{blue}{-308x} & = & \color{red}{308x} +110 \color{blue}{-308x} \color{blue}{-126} \\\Leftrightarrow & -1386x-308x& = & 110-126 \\\Leftrightarrow & \color{red}{-1694} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-1694} & & \\\Leftrightarrow & x = \frac{8}{847} & & \\ & V = \left\{ \frac{8}{847} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & 6x+\frac{10}{7} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1568}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{336}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1568x \color{red}{+147} & = & \color{red}{336x} +80 \\\Leftrightarrow & -1568x \color{red}{+147} \color{blue}{-147} \color{blue}{-336x} & = & \color{red}{336x} +80 \color{blue}{-336x} \color{blue}{-147} \\\Leftrightarrow & -1568x-336x& = & 80-147 \\\Leftrightarrow & \color{red}{-1904} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-1904} & & \\\Leftrightarrow & x = \frac{67}{1904} & & \\ & V = \left\{ \frac{67}{1904} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -30x+35x& = & 6+12 \\\Leftrightarrow & \color{red}{5} x& = & 18 \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & 9x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{16}{7}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+32} & = & \color{red}{126x} +63 \\\Leftrightarrow & 112x \color{red}{+32} \color{blue}{-32} \color{blue}{-126x} & = & \color{red}{126x} +63 \color{blue}{-126x} \color{blue}{-32} \\\Leftrightarrow & 112x-126x& = & 63-32 \\\Leftrightarrow & \color{red}{-14} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-14} & & \\\Leftrightarrow & x = \frac{-31}{14} & & \\ & V = \left\{ \frac{-31}{14} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{2})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{15}{2}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{+75} & = & \color{red}{-30x} +12 \\\Leftrightarrow & 100x \color{red}{+75} \color{blue}{-75} \color{blue}{+30x} & = & \color{red}{-30x} +12 \color{blue}{+30x} \color{blue}{-75} \\\Leftrightarrow & 100x+30x& = & 12-75 \\\Leftrightarrow & \color{red}{130} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{130} & & \\ & V = \left\{ \frac{-63}{130} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+66} & = & \color{red}{-539x} +14 \\\Leftrightarrow & 693x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & 693x+539x& = & 14-66 \\\Leftrightarrow & \color{red}{1232} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{1232} & & \\\Leftrightarrow & x = \frac{-13}{308} & & \\ & V = \left\{ \frac{-13}{308} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -20x-\frac{20}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-20} & = & \color{red}{49x} +2 \\\Leftrightarrow & -140x \color{red}{-20} \color{blue}{+20} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+20} \\\Leftrightarrow & -140x-49x& = & 2+20 \\\Leftrightarrow & \color{red}{-189} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-189} & & \\\Leftrightarrow & x = \frac{-22}{189} & & \\ & V = \left\{ \frac{-22}{189} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{11})& = & -3x+\frac{9}{11} \\\Leftrightarrow & -20x-\frac{16}{11}& = & -3x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{16}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-16} & = & \color{red}{-33x} +9 \\\Leftrightarrow & -220x \color{red}{-16} \color{blue}{+16} \color{blue}{+33x} & = & \color{red}{-33x} +9 \color{blue}{+33x} \color{blue}{+16} \\\Leftrightarrow & -220x+33x& = & 9+16 \\\Leftrightarrow & \color{red}{-187} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-187} & & \\\Leftrightarrow & x = \frac{-25}{187} & & \\ & V = \left\{ \frac{-25}{187} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{3})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-88} & = & \color{red}{-297x} +30 \\\Leftrightarrow & -264x \color{red}{-88} \color{blue}{+88} \color{blue}{+297x} & = & \color{red}{-297x} +30 \color{blue}{+297x} \color{blue}{+88} \\\Leftrightarrow & -264x+297x& = & 30+88 \\\Leftrightarrow & \color{red}{33} x& = & 118 \\\Leftrightarrow & x = \frac{118}{33} & & \\ & V = \left\{ \frac{118}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{9})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{20}{9}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{-40} & = & \color{red}{-90x} +81 \\\Leftrightarrow & -216x \color{red}{-40} \color{blue}{+40} \color{blue}{+90x} & = & \color{red}{-90x} +81 \color{blue}{+90x} \color{blue}{+40} \\\Leftrightarrow & -216x+90x& = & 81+40 \\\Leftrightarrow & \color{red}{-126} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-126} & & \\\Leftrightarrow & x = \frac{-121}{126} & & \\ & V = \left\{ \frac{-121}{126} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+54} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 756x \color{red}{+54} \color{blue}{-54} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-54} \\\Leftrightarrow & 756x+315x& = & 56-54 \\\Leftrightarrow & \color{red}{1071} x& = & 2 \\\Leftrightarrow & x = \frac{2}{1071} & & \\ & V = \left\{ \frac{2}{1071} \right\} & \\\end{align}\)