Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{20}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-100} & = & \color{red}{315x} +42 \\\Leftrightarrow & -280x \color{red}{-100} \color{blue}{+100} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+100} \\\Leftrightarrow & -280x-315x& = & 42+100 \\\Leftrightarrow & \color{red}{-595} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-595} & & \\\Leftrightarrow & x = \frac{-142}{595} & & \\ & V = \left\{ \frac{-142}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-36} & = & \color{red}{-154x} +77 \\\Leftrightarrow & 660x \color{red}{-36} \color{blue}{+36} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{+36} \\\Leftrightarrow & 660x+154x& = & 77+36 \\\Leftrightarrow & \color{red}{814} x& = & 113 \\\Leftrightarrow & x = \frac{113}{814} & & \\ & V = \left\{ \frac{113}{814} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{10}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-30} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -660x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & -660x+231x& = & 110+30 \\\Leftrightarrow & \color{red}{-429} x& = & 140 \\\Leftrightarrow & x = \frac{140}{-429} & & \\\Leftrightarrow & x = \frac{-140}{429} & & \\ & V = \left\{ \frac{-140}{429} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{7})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+220} & = & \color{red}{385x} +21 \\\Leftrightarrow & 1232x \color{red}{+220} \color{blue}{-220} \color{blue}{-385x} & = & \color{red}{385x} +21 \color{blue}{-385x} \color{blue}{-220} \\\Leftrightarrow & 1232x-385x& = & 21-220 \\\Leftrightarrow & \color{red}{847} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{847} & & \\ & V = \left\{ \frac{-199}{847} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 18x+\frac{12}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{+36} & = & \color{red}{105x} +56 \\\Leftrightarrow & 378x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 378x-105x& = & 56-36 \\\Leftrightarrow & \color{red}{273} x& = & 20 \\\Leftrightarrow & x = \frac{20}{273} & & \\ & V = \left\{ \frac{20}{273} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & -8x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -8x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+99} & = & \color{red}{-440x} +40 \\\Leftrightarrow & 825x \color{red}{+99} \color{blue}{-99} \color{blue}{+440x} & = & \color{red}{-440x} +40 \color{blue}{+440x} \color{blue}{-99} \\\Leftrightarrow & 825x+440x& = & 40-99 \\\Leftrightarrow & \color{red}{1265} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{1265} & & \\ & V = \left\{ \frac{-59}{1265} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{4})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 10x-\frac{15}{4}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{200}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 200x \color{red}{-75} & = & \color{red}{140x} +6 \\\Leftrightarrow & 200x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +6 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & 200x-140x& = & 6+75 \\\Leftrightarrow & \color{red}{60} x& = & 81 \\\Leftrightarrow & x = \frac{81}{60} & & \\\Leftrightarrow & x = \frac{27}{20} & & \\ & V = \left\{ \frac{27}{20} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{5})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+8} & = & \color{red}{70x} +9 \\\Leftrightarrow & -100x \color{red}{+8} \color{blue}{-8} \color{blue}{-70x} & = & \color{red}{70x} +9 \color{blue}{-70x} \color{blue}{-8} \\\Leftrightarrow & -100x-70x& = & 9-8 \\\Leftrightarrow & \color{red}{-170} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-170} & & \\\Leftrightarrow & x = \frac{-1}{170} & & \\ & V = \left\{ \frac{-1}{170} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{+36} & = & \color{red}{105x} +50 \\\Leftrightarrow & -135x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -135x-105x& = & 50-36 \\\Leftrightarrow & \color{red}{-240} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-240} & & \\\Leftrightarrow & x = \frac{-7}{120} & & \\ & V = \left\{ \frac{-7}{120} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{9})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 16x-\frac{16}{9}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{112}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-112} & = & \color{red}{-441x} +90 \\\Leftrightarrow & 1008x \color{red}{-112} \color{blue}{+112} \color{blue}{+441x} & = & \color{red}{-441x} +90 \color{blue}{+441x} \color{blue}{+112} \\\Leftrightarrow & 1008x+441x& = & 90+112 \\\Leftrightarrow & \color{red}{1449} x& = & 202 \\\Leftrightarrow & x = \frac{202}{1449} & & \\ & V = \left\{ \frac{202}{1449} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{-45x} +2 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{+45x} & = & \color{red}{-45x} +2 \color{blue}{+45x} \color{blue}{+12} \\\Leftrightarrow & -90x+45x& = & 2+12 \\\Leftrightarrow & \color{red}{-45} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-45} & & \\\Leftrightarrow & x = \frac{-14}{45} & & \\ & V = \left\{ \frac{-14}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{5})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -20x+\frac{16}{5}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x+ \frac{96}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{+96} & = & \color{red}{-90x} +25 \\\Leftrightarrow & -600x \color{red}{+96} \color{blue}{-96} \color{blue}{+90x} & = & \color{red}{-90x} +25 \color{blue}{+90x} \color{blue}{-96} \\\Leftrightarrow & -600x+90x& = & 25-96 \\\Leftrightarrow & \color{red}{-510} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-510} & & \\\Leftrightarrow & x = \frac{71}{510} & & \\ & V = \left\{ \frac{71}{510} \right\} & \\\end{align}\)