Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{9})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 28x-\frac{28}{9}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2772}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{-308} & = & \color{red}{297x} +45 \\\Leftrightarrow & 2772x \color{red}{-308} \color{blue}{+308} \color{blue}{-297x} & = & \color{red}{297x} +45 \color{blue}{-297x} \color{blue}{+308} \\\Leftrightarrow & 2772x-297x& = & 45+308 \\\Leftrightarrow & \color{red}{2475} x& = & 353 \\\Leftrightarrow & x = \frac{353}{2475} & & \\ & V = \left\{ \frac{353}{2475} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{11})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+168} & = & \color{red}{-385x} +99 \\\Leftrightarrow & 924x \color{red}{+168} \color{blue}{-168} \color{blue}{+385x} & = & \color{red}{-385x} +99 \color{blue}{+385x} \color{blue}{-168} \\\Leftrightarrow & 924x+385x& = & 99-168 \\\Leftrightarrow & \color{red}{1309} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{1309} & & \\ & V = \left\{ \frac{-69}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{50x} +45 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & -120x-50x& = & 45-24 \\\Leftrightarrow & \color{red}{-170} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-170} & & \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{8})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{15}{8}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{+75} & = & \color{red}{200x} +48 \\\Leftrightarrow & -480x \color{red}{+75} \color{blue}{-75} \color{blue}{-200x} & = & \color{red}{200x} +48 \color{blue}{-200x} \color{blue}{-75} \\\Leftrightarrow & -480x-200x& = & 48-75 \\\Leftrightarrow & \color{red}{-680} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-680} & & \\\Leftrightarrow & x = \frac{27}{680} & & \\ & V = \left\{ \frac{27}{680} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+105} & = & \color{red}{-252x} +32 \\\Leftrightarrow & 700x \color{red}{+105} \color{blue}{-105} \color{blue}{+252x} & = & \color{red}{-252x} +32 \color{blue}{+252x} \color{blue}{-105} \\\Leftrightarrow & 700x+252x& = & 32-105 \\\Leftrightarrow & \color{red}{952} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{952} & & \\ & V = \left\{ \frac{-73}{952} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{5})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 16x+\frac{8}{5}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+88} & = & \color{red}{-165x} +50 \\\Leftrightarrow & 880x \color{red}{+88} \color{blue}{-88} \color{blue}{+165x} & = & \color{red}{-165x} +50 \color{blue}{+165x} \color{blue}{-88} \\\Leftrightarrow & 880x+165x& = & 50-88 \\\Leftrightarrow & \color{red}{1045} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{1045} & & \\\Leftrightarrow & x = \frac{-2}{55} & & \\ & V = \left\{ \frac{-2}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 2x+\frac{9}{8} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 2x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1008}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{112}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1008x \color{red}{-240} & = & \color{red}{112x} +63 \\\Leftrightarrow & -1008x \color{red}{-240} \color{blue}{+240} \color{blue}{-112x} & = & \color{red}{112x} +63 \color{blue}{-112x} \color{blue}{+240} \\\Leftrightarrow & -1008x-112x& = & 63+240 \\\Leftrightarrow & \color{red}{-1120} x& = & 303 \\\Leftrightarrow & x = \frac{303}{-1120} & & \\\Leftrightarrow & x = \frac{-303}{1120} & & \\ & V = \left\{ \frac{-303}{1120} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 6x-\frac{4}{5}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{-4} & = & \color{red}{25x} +2 \\\Leftrightarrow & 30x \color{red}{-4} \color{blue}{+4} \color{blue}{-25x} & = & \color{red}{25x} +2 \color{blue}{-25x} \color{blue}{+4} \\\Leftrightarrow & 30x-25x& = & 2+4 \\\Leftrightarrow & \color{red}{5} x& = & 6 \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-150} & = & \color{red}{-245x} +56 \\\Leftrightarrow & -1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +56 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & -1050x+245x& = & 56+150 \\\Leftrightarrow & \color{red}{-805} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-805} & & \\\Leftrightarrow & x = \frac{-206}{805} & & \\ & V = \left\{ \frac{-206}{805} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -20x+\frac{8}{9}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+56} & = & \color{red}{-441x} +36 \\\Leftrightarrow & -1260x \color{red}{+56} \color{blue}{-56} \color{blue}{+441x} & = & \color{red}{-441x} +36 \color{blue}{+441x} \color{blue}{-56} \\\Leftrightarrow & -1260x+441x& = & 36-56 \\\Leftrightarrow & \color{red}{-819} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-819} & & \\\Leftrightarrow & x = \frac{20}{819} & & \\ & V = \left\{ \frac{20}{819} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{7})& = & -7x+\frac{3}{8} \\\Leftrightarrow & -20x-\frac{25}{7}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{200}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-200} & = & \color{red}{-392x} +21 \\\Leftrightarrow & -1120x \color{red}{-200} \color{blue}{+200} \color{blue}{+392x} & = & \color{red}{-392x} +21 \color{blue}{+392x} \color{blue}{+200} \\\Leftrightarrow & -1120x+392x& = & 21+200 \\\Leftrightarrow & \color{red}{-728} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-728} & & \\\Leftrightarrow & x = \frac{-17}{56} & & \\ & V = \left\{ \frac{-17}{56} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{10}{3}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+70} & = & \color{red}{-63x} +9 \\\Leftrightarrow & 168x \color{red}{+70} \color{blue}{-70} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{-70} \\\Leftrightarrow & 168x+63x& = & 9-70 \\\Leftrightarrow & \color{red}{231} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{231} & & \\ & V = \left\{ \frac{-61}{231} \right\} & \\\end{align}\)