Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{5})& = & -3x+\frac{9}{8} \\\Leftrightarrow & 16x+\frac{16}{5}& = & -3x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{640}{ \color{blue}{40} }x+ \frac{128}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 640x \color{red}{+128} & = & \color{red}{-120x} +45 \\\Leftrightarrow & 640x \color{red}{+128} \color{blue}{-128} \color{blue}{+120x} & = & \color{red}{-120x} +45 \color{blue}{+120x} \color{blue}{-128} \\\Leftrightarrow & 640x+120x& = & 45-128 \\\Leftrightarrow & \color{red}{760} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{760} & & \\ & V = \left\{ \frac{-83}{760} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -16x-\frac{12}{11}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-84} & = & \color{red}{-539x} +33 \\\Leftrightarrow & -1232x \color{red}{-84} \color{blue}{+84} \color{blue}{+539x} & = & \color{red}{-539x} +33 \color{blue}{+539x} \color{blue}{+84} \\\Leftrightarrow & -1232x+539x& = & 33+84 \\\Leftrightarrow & \color{red}{-693} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-693} & & \\\Leftrightarrow & x = \frac{-13}{77} & & \\ & V = \left\{ \frac{-13}{77} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -10x+\frac{15}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+75} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -350x \color{red}{+75} \color{blue}{-75} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{-75} \\\Leftrightarrow & -350x+245x& = & 28-75 \\\Leftrightarrow & \color{red}{-105} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-105} & & \\\Leftrightarrow & x = \frac{47}{105} & & \\ & V = \left\{ \frac{47}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{5})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-600}{ \color{blue}{20} }x- \frac{96}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -600x \color{red}{-96} & = & \color{red}{140x} +25 \\\Leftrightarrow & -600x \color{red}{-96} \color{blue}{+96} \color{blue}{-140x} & = & \color{red}{140x} +25 \color{blue}{-140x} \color{blue}{+96} \\\Leftrightarrow & -600x-140x& = & 25+96 \\\Leftrightarrow & \color{red}{-740} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-740} & & \\\Leftrightarrow & x = \frac{-121}{740} & & \\ & V = \left\{ \frac{-121}{740} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{9})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{16}{9}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+16} & = & \color{red}{81x} +24 \\\Leftrightarrow & 72x \color{red}{+16} \color{blue}{-16} \color{blue}{-81x} & = & \color{red}{81x} +24 \color{blue}{-81x} \color{blue}{-16} \\\Leftrightarrow & 72x-81x& = & 24-16 \\\Leftrightarrow & \color{red}{-9} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-9} & & \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{15}{4}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{+45} & = & \color{red}{-60x} +16 \\\Leftrightarrow & 72x \color{red}{+45} \color{blue}{-45} \color{blue}{+60x} & = & \color{red}{-60x} +16 \color{blue}{+60x} \color{blue}{-45} \\\Leftrightarrow & 72x+60x& = & 16-45 \\\Leftrightarrow & \color{red}{132} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{132} & & \\ & V = \left\{ \frac{-29}{132} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{9})& = & 6x+\frac{8}{7} \\\Leftrightarrow & 25x-\frac{20}{9}& = & 6x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{378}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{-140} & = & \color{red}{378x} +72 \\\Leftrightarrow & 1575x \color{red}{-140} \color{blue}{+140} \color{blue}{-378x} & = & \color{red}{378x} +72 \color{blue}{-378x} \color{blue}{+140} \\\Leftrightarrow & 1575x-378x& = & 72+140 \\\Leftrightarrow & \color{red}{1197} x& = & 212 \\\Leftrightarrow & x = \frac{212}{1197} & & \\ & V = \left\{ \frac{212}{1197} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{3})& = & 3x+\frac{5}{7} \\\Leftrightarrow & -14x-\frac{28}{3}& = & 3x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{-196} & = & \color{red}{63x} +15 \\\Leftrightarrow & -294x \color{red}{-196} \color{blue}{+196} \color{blue}{-63x} & = & \color{red}{63x} +15 \color{blue}{-63x} \color{blue}{+196} \\\Leftrightarrow & -294x-63x& = & 15+196 \\\Leftrightarrow & \color{red}{-357} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-357} & & \\\Leftrightarrow & x = \frac{-211}{357} & & \\ & V = \left\{ \frac{-211}{357} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{6}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{315x} +14 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{+54} \\\Leftrightarrow & 504x-315x& = & 14+54 \\\Leftrightarrow & \color{red}{189} x& = & 68 \\\Leftrightarrow & x = \frac{68}{189} & & \\ & V = \left\{ \frac{68}{189} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{9})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{4}{9}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{-4} & = & \color{red}{45x} +30 \\\Leftrightarrow & 54x \color{red}{-4} \color{blue}{+4} \color{blue}{-45x} & = & \color{red}{45x} +30 \color{blue}{-45x} \color{blue}{+4} \\\Leftrightarrow & 54x-45x& = & 30+4 \\\Leftrightarrow & \color{red}{9} x& = & 34 \\\Leftrightarrow & x = \frac{34}{9} & & \\ & V = \left\{ \frac{34}{9} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{11})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -9x-\frac{15}{11}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1188}{ \color{blue}{132} }x- \frac{180}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1188x \color{red}{-180} & = & \color{red}{-660x} +55 \\\Leftrightarrow & -1188x \color{red}{-180} \color{blue}{+180} \color{blue}{+660x} & = & \color{red}{-660x} +55 \color{blue}{+660x} \color{blue}{+180} \\\Leftrightarrow & -1188x+660x& = & 55+180 \\\Leftrightarrow & \color{red}{-528} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-528} & & \\\Leftrightarrow & x = \frac{-235}{528} & & \\ & V = \left\{ \frac{-235}{528} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{11})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -16x+\frac{16}{11}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1408}{ \color{blue}{88} }x+ \frac{128}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1408x \color{red}{+128} & = & \color{red}{616x} +55 \\\Leftrightarrow & -1408x \color{red}{+128} \color{blue}{-128} \color{blue}{-616x} & = & \color{red}{616x} +55 \color{blue}{-616x} \color{blue}{-128} \\\Leftrightarrow & -1408x-616x& = & 55-128 \\\Leftrightarrow & \color{red}{-2024} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-2024} & & \\\Leftrightarrow & x = \frac{73}{2024} & & \\ & V = \left\{ \frac{73}{2024} \right\} & \\\end{align}\)