Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -9x+\frac{15}{4}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-324}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -324x \color{red}{+135} & = & \color{red}{180x} +16 \\\Leftrightarrow & -324x \color{red}{+135} \color{blue}{-135} \color{blue}{-180x} & = & \color{red}{180x} +16 \color{blue}{-180x} \color{blue}{-135} \\\Leftrightarrow & -324x-180x& = & 16-135 \\\Leftrightarrow & \color{red}{-504} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-504} & & \\\Leftrightarrow & x = \frac{17}{72} & & \\ & V = \left\{ \frac{17}{72} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{8}{3}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{+16} & = & \color{red}{42x} +9 \\\Leftrightarrow & 60x \color{red}{+16} \color{blue}{-16} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{-16} \\\Leftrightarrow & 60x-42x& = & 9-16 \\\Leftrightarrow & \color{red}{18} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{18} & & \\ & V = \left\{ \frac{-7}{18} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & 3x+\frac{5}{12} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{840}{ \color{blue}{84} }x- \frac{120}{ \color{blue}{84} })& = & (\frac{252}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 840x \color{red}{-120} & = & \color{red}{252x} +35 \\\Leftrightarrow & 840x \color{red}{-120} \color{blue}{+120} \color{blue}{-252x} & = & \color{red}{252x} +35 \color{blue}{-252x} \color{blue}{+120} \\\Leftrightarrow & 840x-252x& = & 35+120 \\\Leftrightarrow & \color{red}{588} x& = & 155 \\\Leftrightarrow & x = \frac{155}{588} & & \\ & V = \left\{ \frac{155}{588} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{4})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{15}{4}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+45} & = & \color{red}{-36x} +32 \\\Leftrightarrow & -300x \color{red}{+45} \color{blue}{-45} \color{blue}{+36x} & = & \color{red}{-36x} +32 \color{blue}{+36x} \color{blue}{-45} \\\Leftrightarrow & -300x+36x& = & 32-45 \\\Leftrightarrow & \color{red}{-264} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-264} & & \\\Leftrightarrow & x = \frac{13}{264} & & \\ & V = \left\{ \frac{13}{264} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{11})& = & -8x+\frac{4}{3} \\\Leftrightarrow & 9x-\frac{15}{11}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{-45} & = & \color{red}{-264x} +44 \\\Leftrightarrow & 297x \color{red}{-45} \color{blue}{+45} \color{blue}{+264x} & = & \color{red}{-264x} +44 \color{blue}{+264x} \color{blue}{+45} \\\Leftrightarrow & 297x+264x& = & 44+45 \\\Leftrightarrow & \color{red}{561} x& = & 89 \\\Leftrightarrow & x = \frac{89}{561} & & \\ & V = \left\{ \frac{89}{561} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+96} & = & \color{red}{-200x} +35 \\\Leftrightarrow & 480x \color{red}{+96} \color{blue}{-96} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{-96} \\\Leftrightarrow & 480x+200x& = & 35-96 \\\Leftrightarrow & \color{red}{680} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{680} & & \\ & V = \left\{ \frac{-61}{680} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{11})& = & 8x+\frac{8}{3} \\\Leftrightarrow & 35x+\frac{28}{11}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{84}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+84} & = & \color{red}{264x} +88 \\\Leftrightarrow & 1155x \color{red}{+84} \color{blue}{-84} \color{blue}{-264x} & = & \color{red}{264x} +88 \color{blue}{-264x} \color{blue}{-84} \\\Leftrightarrow & 1155x-264x& = & 88-84 \\\Leftrightarrow & \color{red}{891} x& = & 4 \\\Leftrightarrow & x = \frac{4}{891} & & \\ & V = \left\{ \frac{4}{891} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{7})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 30x+\frac{12}{7}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1680}{ \color{blue}{56} }x+ \frac{96}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1680x \color{red}{+96} & = & \color{red}{392x} +49 \\\Leftrightarrow & 1680x \color{red}{+96} \color{blue}{-96} \color{blue}{-392x} & = & \color{red}{392x} +49 \color{blue}{-392x} \color{blue}{-96} \\\Leftrightarrow & 1680x-392x& = & 49-96 \\\Leftrightarrow & \color{red}{1288} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{1288} & & \\ & V = \left\{ \frac{-47}{1288} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{11})& = & -9x+\frac{5}{3} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+24} & = & \color{red}{-297x} +55 \\\Leftrightarrow & -264x \color{red}{+24} \color{blue}{-24} \color{blue}{+297x} & = & \color{red}{-297x} +55 \color{blue}{+297x} \color{blue}{-24} \\\Leftrightarrow & -264x+297x& = & 55-24 \\\Leftrightarrow & \color{red}{33} x& = & 31 \\\Leftrightarrow & x = \frac{31}{33} & & \\ & V = \left\{ \frac{31}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+84} & = & \color{red}{245x} +20 \\\Leftrightarrow & 1050x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & 1050x-245x& = & 20-84 \\\Leftrightarrow & \color{red}{805} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{805} & & \\ & V = \left\{ \frac{-64}{805} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+66} & = & \color{red}{-385x} +49 \\\Leftrightarrow & 693x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +49 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & 693x+385x& = & 49-66 \\\Leftrightarrow & \color{red}{1078} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{1078} & & \\ & V = \left\{ \frac{-17}{1078} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 6x-\frac{9}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{45}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-45} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 210x \color{red}{-45} \color{blue}{+45} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{+45} \\\Leftrightarrow & 210x+175x& = & 28+45 \\\Leftrightarrow & \color{red}{385} x& = & 73 \\\Leftrightarrow & x = \frac{73}{385} & & \\ & V = \left\{ \frac{73}{385} \right\} & \\\end{align}\)