Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 180x+75x& = & 40+36 \\\Leftrightarrow & \color{red}{255} x& = & 76 \\\Leftrightarrow & x = \frac{76}{255} & & \\ & V = \left\{ \frac{76}{255} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{9}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+9} & = & \color{red}{35x} +6 \\\Leftrightarrow & -30x \color{red}{+9} \color{blue}{-9} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-9} \\\Leftrightarrow & -30x-35x& = & 6-9 \\\Leftrightarrow & \color{red}{-65} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-65} & & \\\Leftrightarrow & x = \frac{3}{65} & & \\ & V = \left\{ \frac{3}{65} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{-100} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -560x \color{red}{-100} \color{blue}{+100} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+100} \\\Leftrightarrow & -560x+245x& = & 42+100 \\\Leftrightarrow & \color{red}{-315} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-315} & & \\\Leftrightarrow & x = \frac{-142}{315} & & \\ & V = \left\{ \frac{-142}{315} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{35}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{385}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+385} & = & \color{red}{-297x} +54 \\\Leftrightarrow & -1386x \color{red}{+385} \color{blue}{-385} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{-385} \\\Leftrightarrow & -1386x+297x& = & 54-385 \\\Leftrightarrow & \color{red}{-1089} x& = & -331 \\\Leftrightarrow & x = \frac{-331}{-1089} & & \\\Leftrightarrow & x = \frac{331}{1089} & & \\ & V = \left\{ \frac{331}{1089} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{10}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+30} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 198x \color{red}{+30} \color{blue}{-30} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-30} \\\Leftrightarrow & 198x+231x& = & 88-30 \\\Leftrightarrow & \color{red}{429} x& = & 58 \\\Leftrightarrow & x = \frac{58}{429} & & \\ & V = \left\{ \frac{58}{429} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{3})& = & 8x+\frac{7}{10} \\\Leftrightarrow & -21x-\frac{35}{3}& = & 8x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x- \frac{350}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{-350} & = & \color{red}{240x} +21 \\\Leftrightarrow & -630x \color{red}{-350} \color{blue}{+350} \color{blue}{-240x} & = & \color{red}{240x} +21 \color{blue}{-240x} \color{blue}{+350} \\\Leftrightarrow & -630x-240x& = & 21+350 \\\Leftrightarrow & \color{red}{-870} x& = & 371 \\\Leftrightarrow & x = \frac{371}{-870} & & \\\Leftrightarrow & x = \frac{-371}{870} & & \\ & V = \left\{ \frac{-371}{870} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -10x+\frac{20}{3}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+60} & = & \color{red}{63x} +5 \\\Leftrightarrow & -90x \color{red}{+60} \color{blue}{-60} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{-60} \\\Leftrightarrow & -90x-63x& = & 5-60 \\\Leftrightarrow & \color{red}{-153} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-153} & & \\\Leftrightarrow & x = \frac{55}{153} & & \\ & V = \left\{ \frac{55}{153} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{25}{6}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{660}{ \color{blue}{66} }x- \frac{275}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{24}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 660x \color{red}{-275} & = & \color{red}{-462x} +24 \\\Leftrightarrow & 660x \color{red}{-275} \color{blue}{+275} \color{blue}{+462x} & = & \color{red}{-462x} +24 \color{blue}{+462x} \color{blue}{+275} \\\Leftrightarrow & 660x+462x& = & 24+275 \\\Leftrightarrow & \color{red}{1122} x& = & 299 \\\Leftrightarrow & x = \frac{299}{1122} & & \\ & V = \left\{ \frac{299}{1122} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{135x} +10 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{-36} \\\Leftrightarrow & -120x-135x& = & 10-36 \\\Leftrightarrow & \color{red}{-255} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-255} & & \\\Leftrightarrow & x = \frac{26}{255} & & \\ & V = \left\{ \frac{26}{255} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+110} & = & \color{red}{231x} +42 \\\Leftrightarrow & 1540x \color{red}{+110} \color{blue}{-110} \color{blue}{-231x} & = & \color{red}{231x} +42 \color{blue}{-231x} \color{blue}{-110} \\\Leftrightarrow & 1540x-231x& = & 42-110 \\\Leftrightarrow & \color{red}{1309} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{1309} & & \\\Leftrightarrow & x = \frac{-4}{77} & & \\ & V = \left\{ \frac{-4}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{21}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+63} & = & \color{red}{-99x} +88 \\\Leftrightarrow & -1155x \color{red}{+63} \color{blue}{-63} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{-63} \\\Leftrightarrow & -1155x+99x& = & 88-63 \\\Leftrightarrow & \color{red}{-1056} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-1056} & & \\\Leftrightarrow & x = \frac{-25}{1056} & & \\ & V = \left\{ \frac{-25}{1056} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -16x-\frac{16}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-352}{ \color{blue}{22} }x- \frac{32}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -352x \color{red}{-32} & = & \color{red}{154x} +77 \\\Leftrightarrow & -352x \color{red}{-32} \color{blue}{+32} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{+32} \\\Leftrightarrow & -352x-154x& = & 77+32 \\\Leftrightarrow & \color{red}{-506} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-506} & & \\\Leftrightarrow & x = \frac{-109}{506} & & \\ & V = \left\{ \frac{-109}{506} \right\} & \\\end{align}\)