Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{-49x} +3 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -70x+49x& = & 3+10 \\\Leftrightarrow & \color{red}{-21} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-21} & & \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{8})& = & 4x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{+45} & = & \color{red}{96x} +32 \\\Leftrightarrow & -360x \color{red}{+45} \color{blue}{-45} \color{blue}{-96x} & = & \color{red}{96x} +32 \color{blue}{-96x} \color{blue}{-45} \\\Leftrightarrow & -360x-96x& = & 32-45 \\\Leftrightarrow & \color{red}{-456} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-456} & & \\\Leftrightarrow & x = \frac{13}{456} & & \\ & V = \left\{ \frac{13}{456} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{11})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{15}{11}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x+ \frac{150}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{+150} & = & \color{red}{-770x} +33 \\\Leftrightarrow & -2200x \color{red}{+150} \color{blue}{-150} \color{blue}{+770x} & = & \color{red}{-770x} +33 \color{blue}{+770x} \color{blue}{-150} \\\Leftrightarrow & -2200x+770x& = & 33-150 \\\Leftrightarrow & \color{red}{-1430} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{-1430} & & \\\Leftrightarrow & x = \frac{9}{110} & & \\ & V = \left\{ \frac{9}{110} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -6x+\frac{4}{5}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+28} & = & \color{red}{245x} +10 \\\Leftrightarrow & -210x \color{red}{+28} \color{blue}{-28} \color{blue}{-245x} & = & \color{red}{245x} +10 \color{blue}{-245x} \color{blue}{-28} \\\Leftrightarrow & -210x-245x& = & 10-28 \\\Leftrightarrow & \color{red}{-455} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-455} & & \\\Leftrightarrow & x = \frac{18}{455} & & \\ & V = \left\{ \frac{18}{455} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{4})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{+30} & = & \color{red}{40x} +7 \\\Leftrightarrow & -96x \color{red}{+30} \color{blue}{-30} \color{blue}{-40x} & = & \color{red}{40x} +7 \color{blue}{-40x} \color{blue}{-30} \\\Leftrightarrow & -96x-40x& = & 7-30 \\\Leftrightarrow & \color{red}{-136} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-136} & & \\\Leftrightarrow & x = \frac{23}{136} & & \\ & V = \left\{ \frac{23}{136} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{3})& = & -9x+\frac{5}{8} \\\Leftrightarrow & -25x+\frac{10}{3}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+80} & = & \color{red}{-216x} +15 \\\Leftrightarrow & -600x \color{red}{+80} \color{blue}{-80} \color{blue}{+216x} & = & \color{red}{-216x} +15 \color{blue}{+216x} \color{blue}{-80} \\\Leftrightarrow & -600x+216x& = & 15-80 \\\Leftrightarrow & \color{red}{-384} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-384} & & \\\Leftrightarrow & x = \frac{65}{384} & & \\ & V = \left\{ \frac{65}{384} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & 9x+\frac{2}{5} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-40} & = & \color{red}{405x} +18 \\\Leftrightarrow & 180x \color{red}{-40} \color{blue}{+40} \color{blue}{-405x} & = & \color{red}{405x} +18 \color{blue}{-405x} \color{blue}{+40} \\\Leftrightarrow & 180x-405x& = & 18+40 \\\Leftrightarrow & \color{red}{-225} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-225} & & \\\Leftrightarrow & x = \frac{-58}{225} & & \\ & V = \left\{ \frac{-58}{225} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{11})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 14x-\frac{21}{11}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{924}{ \color{blue}{66} }x- \frac{126}{ \color{blue}{66} })& = & (\frac{594}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 924x \color{red}{-126} & = & \color{red}{594x} +55 \\\Leftrightarrow & 924x \color{red}{-126} \color{blue}{+126} \color{blue}{-594x} & = & \color{red}{594x} +55 \color{blue}{-594x} \color{blue}{+126} \\\Leftrightarrow & 924x-594x& = & 55+126 \\\Leftrightarrow & \color{red}{330} x& = & 181 \\\Leftrightarrow & x = \frac{181}{330} & & \\ & V = \left\{ \frac{181}{330} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{3})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+100} & = & \color{red}{135x} +24 \\\Leftrightarrow & 150x \color{red}{+100} \color{blue}{-100} \color{blue}{-135x} & = & \color{red}{135x} +24 \color{blue}{-135x} \color{blue}{-100} \\\Leftrightarrow & 150x-135x& = & 24-100 \\\Leftrightarrow & \color{red}{15} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{15} & & \\ & V = \left\{ \frac{-76}{15} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{5})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-200}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -200x \color{red}{+16} & = & \color{red}{140x} +45 \\\Leftrightarrow & -200x \color{red}{+16} \color{blue}{-16} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{-16} \\\Leftrightarrow & -200x-140x& = & 45-16 \\\Leftrightarrow & \color{red}{-340} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-340} & & \\\Leftrightarrow & x = \frac{-29}{340} & & \\ & V = \left\{ \frac{-29}{340} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{4})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -15x-\frac{9}{4}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{99}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-99} & = & \color{red}{-176x} +8 \\\Leftrightarrow & -660x \color{red}{-99} \color{blue}{+99} \color{blue}{+176x} & = & \color{red}{-176x} +8 \color{blue}{+176x} \color{blue}{+99} \\\Leftrightarrow & -660x+176x& = & 8+99 \\\Leftrightarrow & \color{red}{-484} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-484} & & \\\Leftrightarrow & x = \frac{-107}{484} & & \\ & V = \left\{ \frac{-107}{484} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{11})& = & -9x+\frac{8}{11} \\\Leftrightarrow & 14x+\frac{14}{11}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{154}{ \color{blue}{11} }x+ \frac{14}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 154x \color{red}{+14} & = & \color{red}{-99x} +8 \\\Leftrightarrow & 154x \color{red}{+14} \color{blue}{-14} \color{blue}{+99x} & = & \color{red}{-99x} +8 \color{blue}{+99x} \color{blue}{-14} \\\Leftrightarrow & 154x+99x& = & 8-14 \\\Leftrightarrow & \color{red}{253} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{253} & & \\ & V = \left\{ \frac{-6}{253} \right\} & \\\end{align}\)