Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{3})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 4x+\frac{10}{3}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{12}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 12x \color{red}{+10} & = & \color{red}{9x} +4 \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{-10} \\\Leftrightarrow & 12x-9x& = & 4-10 \\\Leftrightarrow & \color{red}{3} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{3} & & \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & 6x+\frac{8}{11} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 6x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{528}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{+231} & = & \color{red}{528x} +64 \\\Leftrightarrow & -3080x \color{red}{+231} \color{blue}{-231} \color{blue}{-528x} & = & \color{red}{528x} +64 \color{blue}{-528x} \color{blue}{-231} \\\Leftrightarrow & -3080x-528x& = & 64-231 \\\Leftrightarrow & \color{red}{-3608} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{-3608} & & \\\Leftrightarrow & x = \frac{167}{3608} & & \\ & V = \left\{ \frac{167}{3608} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -4x+\frac{4}{3}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{+8} & = & \color{red}{-30x} +9 \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{-8} \\\Leftrightarrow & -24x+30x& = & 9-8 \\\Leftrightarrow & \color{red}{6} x& = & 1 \\\Leftrightarrow & x = \frac{1}{6} & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{4})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{25}{4}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x+ \frac{225}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{+225} & = & \color{red}{-252x} +8 \\\Leftrightarrow & 720x \color{red}{+225} \color{blue}{-225} \color{blue}{+252x} & = & \color{red}{-252x} +8 \color{blue}{+252x} \color{blue}{-225} \\\Leftrightarrow & 720x+252x& = & 8-225 \\\Leftrightarrow & \color{red}{972} x& = & -217 \\\Leftrightarrow & x = \frac{-217}{972} & & \\ & V = \left\{ \frac{-217}{972} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{8}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{+16} & = & \color{red}{70x} +63 \\\Leftrightarrow & 112x \color{red}{+16} \color{blue}{-16} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{-16} \\\Leftrightarrow & 112x-70x& = & 63-16 \\\Leftrightarrow & \color{red}{42} x& = & 47 \\\Leftrightarrow & x = \frac{47}{42} & & \\ & V = \left\{ \frac{47}{42} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{30}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-30} & = & \color{red}{55x} +6 \\\Leftrightarrow & 132x \color{red}{-30} \color{blue}{+30} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+30} \\\Leftrightarrow & 132x-55x& = & 6+30 \\\Leftrightarrow & \color{red}{77} x& = & 36 \\\Leftrightarrow & x = \frac{36}{77} & & \\ & V = \left\{ \frac{36}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{11})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{+10} & = & \color{red}{77x} +8 \\\Leftrightarrow & 110x \color{red}{+10} \color{blue}{-10} \color{blue}{-77x} & = & \color{red}{77x} +8 \color{blue}{-77x} \color{blue}{-10} \\\Leftrightarrow & 110x-77x& = & 8-10 \\\Leftrightarrow & \color{red}{33} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{33} & & \\ & V = \left\{ \frac{-2}{33} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{5}{4} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{-48} & = & \color{red}{-100x} +25 \\\Leftrightarrow & 240x \color{red}{-48} \color{blue}{+48} \color{blue}{+100x} & = & \color{red}{-100x} +25 \color{blue}{+100x} \color{blue}{+48} \\\Leftrightarrow & 240x+100x& = & 25+48 \\\Leftrightarrow & \color{red}{340} x& = & 73 \\\Leftrightarrow & x = \frac{73}{340} & & \\ & V = \left\{ \frac{73}{340} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{11})& = & 3x+\frac{8}{7} \\\Leftrightarrow & -20x+\frac{16}{11}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+112} & = & \color{red}{231x} +88 \\\Leftrightarrow & -1540x \color{red}{+112} \color{blue}{-112} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-112} \\\Leftrightarrow & -1540x-231x& = & 88-112 \\\Leftrightarrow & \color{red}{-1771} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-1771} & & \\\Leftrightarrow & x = \frac{24}{1771} & & \\ & V = \left\{ \frac{24}{1771} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{15}{8}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{+45} & = & \color{red}{-168x} +32 \\\Leftrightarrow & -240x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +32 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & -240x+168x& = & 32-45 \\\Leftrightarrow & \color{red}{-72} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-72} & & \\\Leftrightarrow & x = \frac{13}{72} & & \\ & V = \left\{ \frac{13}{72} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 3x+\frac{3}{5} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 3x+\frac{3}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{24}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{120x} +24 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{-120x} & = & \color{red}{120x} +24 \color{blue}{-120x} \color{blue}{-105} \\\Leftrightarrow & -560x-120x& = & 24-105 \\\Leftrightarrow & \color{red}{-680} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-680} & & \\\Leftrightarrow & x = \frac{81}{680} & & \\ & V = \left\{ \frac{81}{680} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{11})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 8x+\frac{6}{11}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{880}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 880x \color{red}{+60} & = & \color{red}{-330x} +33 \\\Leftrightarrow & 880x \color{red}{+60} \color{blue}{-60} \color{blue}{+330x} & = & \color{red}{-330x} +33 \color{blue}{+330x} \color{blue}{-60} \\\Leftrightarrow & 880x+330x& = & 33-60 \\\Leftrightarrow & \color{red}{1210} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{1210} & & \\ & V = \left\{ \frac{-27}{1210} \right\} & \\\end{align}\)