Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{2})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{9}{2}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{12}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 12x \color{red}{+9} & = & \color{red}{-10x} +9 \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{+10x} & = & \color{red}{-10x} +9 \color{blue}{+10x} \color{blue}{-9} \\\Leftrightarrow & 12x+10x& = & 9-9 \\\Leftrightarrow & \color{red}{22} x& = & 0 \\\Leftrightarrow & x = \frac{0}{22} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -25x-\frac{10}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-350}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -350x \color{red}{-20} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -350x \color{red}{-20} \color{blue}{+20} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+20} \\\Leftrightarrow & -350x+70x& = & 63+20 \\\Leftrightarrow & \color{red}{-280} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-280} & & \\\Leftrightarrow & x = \frac{-83}{280} & & \\ & V = \left\{ \frac{-83}{280} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{16}{3}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{48}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+48} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 108x \color{red}{+48} \color{blue}{-48} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{-48} \\\Leftrightarrow & 108x+45x& = & 10-48 \\\Leftrightarrow & \color{red}{153} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{153} & & \\ & V = \left\{ \frac{-38}{153} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+40} & = & \color{red}{54x} +9 \\\Leftrightarrow & -48x \color{red}{+40} \color{blue}{-40} \color{blue}{-54x} & = & \color{red}{54x} +9 \color{blue}{-54x} \color{blue}{-40} \\\Leftrightarrow & -48x-54x& = & 9-40 \\\Leftrightarrow & \color{red}{-102} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-102} & & \\\Leftrightarrow & x = \frac{31}{102} & & \\ & V = \left\{ \frac{31}{102} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{11})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 6x+\frac{10}{11}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+30} & = & \color{red}{-165x} +55 \\\Leftrightarrow & 198x \color{red}{+30} \color{blue}{-30} \color{blue}{+165x} & = & \color{red}{-165x} +55 \color{blue}{+165x} \color{blue}{-30} \\\Leftrightarrow & 198x+165x& = & 55-30 \\\Leftrightarrow & \color{red}{363} x& = & 25 \\\Leftrightarrow & x = \frac{25}{363} & & \\ & V = \left\{ \frac{25}{363} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{2})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{15}{2}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-165} & = & \color{red}{154x} +10 \\\Leftrightarrow & -220x \color{red}{-165} \color{blue}{+165} \color{blue}{-154x} & = & \color{red}{154x} +10 \color{blue}{-154x} \color{blue}{+165} \\\Leftrightarrow & -220x-154x& = & 10+165 \\\Leftrightarrow & \color{red}{-374} x& = & 175 \\\Leftrightarrow & x = \frac{175}{-374} & & \\\Leftrightarrow & x = \frac{-175}{374} & & \\ & V = \left\{ \frac{-175}{374} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{5})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -35x+\frac{14}{5}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-175}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -175x \color{red}{+14} & = & \color{red}{15x} +6 \\\Leftrightarrow & -175x \color{red}{+14} \color{blue}{-14} \color{blue}{-15x} & = & \color{red}{15x} +6 \color{blue}{-15x} \color{blue}{-14} \\\Leftrightarrow & -175x-15x& = & 6-14 \\\Leftrightarrow & \color{red}{-190} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-190} & & \\\Leftrightarrow & x = \frac{4}{95} & & \\ & V = \left\{ \frac{4}{95} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{9}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+63} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -420x \color{red}{+63} \color{blue}{-63} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{-63} \\\Leftrightarrow & -420x+175x& = & 15-63 \\\Leftrightarrow & \color{red}{-245} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-245} & & \\\Leftrightarrow & x = \frac{48}{245} & & \\ & V = \left\{ \frac{48}{245} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-66} & = & \color{red}{-385x} +42 \\\Leftrightarrow & -924x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & -924x+385x& = & 42+66 \\\Leftrightarrow & \color{red}{-539} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-539} & & \\\Leftrightarrow & x = \frac{-108}{539} & & \\ & V = \left\{ \frac{-108}{539} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+154} & = & \color{red}{-99x} +30 \\\Leftrightarrow & 462x \color{red}{+154} \color{blue}{-154} \color{blue}{+99x} & = & \color{red}{-99x} +30 \color{blue}{+99x} \color{blue}{-154} \\\Leftrightarrow & 462x+99x& = & 30-154 \\\Leftrightarrow & \color{red}{561} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{561} & & \\ & V = \left\{ \frac{-124}{561} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{3})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{4}{3}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{20}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-20} & = & \color{red}{135x} +18 \\\Leftrightarrow & 120x \color{red}{-20} \color{blue}{+20} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{+20} \\\Leftrightarrow & 120x-135x& = & 18+20 \\\Leftrightarrow & \color{red}{-15} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-15} & & \\\Leftrightarrow & x = \frac{-38}{15} & & \\ & V = \left\{ \frac{-38}{15} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{480}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 480x \color{red}{+48} & = & \color{red}{100x} +45 \\\Leftrightarrow & 480x \color{red}{+48} \color{blue}{-48} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{-48} \\\Leftrightarrow & 480x-100x& = & 45-48 \\\Leftrightarrow & \color{red}{380} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{380} & & \\ & V = \left\{ \frac{-3}{380} \right\} & \\\end{align}\)