Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{20}{7}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-220} & = & \color{red}{-385x} +28 \\\Leftrightarrow & -924x \color{red}{-220} \color{blue}{+220} \color{blue}{+385x} & = & \color{red}{-385x} +28 \color{blue}{+385x} \color{blue}{+220} \\\Leftrightarrow & -924x+385x& = & 28+220 \\\Leftrightarrow & \color{red}{-539} x& = & 248 \\\Leftrightarrow & x = \frac{248}{-539} & & \\\Leftrightarrow & x = \frac{-248}{539} & & \\ & V = \left\{ \frac{-248}{539} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x-\frac{15}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-45} & = & \color{red}{-105x} +35 \\\Leftrightarrow & 252x \color{red}{-45} \color{blue}{+45} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{+45} \\\Leftrightarrow & 252x+105x& = & 35+45 \\\Leftrightarrow & \color{red}{357} x& = & 80 \\\Leftrightarrow & x = \frac{80}{357} & & \\ & V = \left\{ \frac{80}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{4})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{+45} & = & \color{red}{60x} +8 \\\Leftrightarrow & -144x \color{red}{+45} \color{blue}{-45} \color{blue}{-60x} & = & \color{red}{60x} +8 \color{blue}{-60x} \color{blue}{-45} \\\Leftrightarrow & -144x-60x& = & 8-45 \\\Leftrightarrow & \color{red}{-204} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-204} & & \\\Leftrightarrow & x = \frac{37}{204} & & \\ & V = \left\{ \frac{37}{204} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{420}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 420x \color{red}{-36} & = & \color{red}{-294x} +35 \\\Leftrightarrow & 420x \color{red}{-36} \color{blue}{+36} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{+36} \\\Leftrightarrow & 420x+294x& = & 35+36 \\\Leftrightarrow & \color{red}{714} x& = & 71 \\\Leftrightarrow & x = \frac{71}{714} & & \\ & V = \left\{ \frac{71}{714} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{11})& = & 6x+\frac{7}{8} \\\Leftrightarrow & -35x-\frac{28}{11}& = & 6x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x- \frac{224}{ \color{blue}{88} })& = & (\frac{528}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{-224} & = & \color{red}{528x} +77 \\\Leftrightarrow & -3080x \color{red}{-224} \color{blue}{+224} \color{blue}{-528x} & = & \color{red}{528x} +77 \color{blue}{-528x} \color{blue}{+224} \\\Leftrightarrow & -3080x-528x& = & 77+224 \\\Leftrightarrow & \color{red}{-3608} x& = & 301 \\\Leftrightarrow & x = \frac{301}{-3608} & & \\\Leftrightarrow & x = \frac{-301}{3608} & & \\ & V = \left\{ \frac{-301}{3608} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{3})& = & -8x+\frac{6}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{-264x} +18 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+264x} & = & \color{red}{-264x} +18 \color{blue}{+264x} \color{blue}{+154} \\\Leftrightarrow & 1155x+264x& = & 18+154 \\\Leftrightarrow & \color{red}{1419} x& = & 172 \\\Leftrightarrow & x = \frac{172}{1419} & & \\\Leftrightarrow & x = \frac{4}{33} & & \\ & V = \left\{ \frac{4}{33} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{16}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x+ \frac{80}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{+80} & = & \color{red}{315x} +54 \\\Leftrightarrow & -720x \color{red}{+80} \color{blue}{-80} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{-80} \\\Leftrightarrow & -720x-315x& = & 54-80 \\\Leftrightarrow & \color{red}{-1035} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-1035} & & \\\Leftrightarrow & x = \frac{26}{1035} & & \\ & V = \left\{ \frac{26}{1035} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{30x} +10 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{-30x} & = & \color{red}{30x} +10 \color{blue}{-30x} \color{blue}{-36} \\\Leftrightarrow & 135x-30x& = & 10-36 \\\Leftrightarrow & \color{red}{105} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{105} & & \\ & V = \left\{ \frac{-26}{105} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+108} & = & \color{red}{-315x} +40 \\\Leftrightarrow & -270x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -270x+315x& = & 40-108 \\\Leftrightarrow & \color{red}{45} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{45} & & \\ & V = \left\{ \frac{-68}{45} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{-140x} +24 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{-75} \\\Leftrightarrow & -120x+140x& = & 24-75 \\\Leftrightarrow & \color{red}{20} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{20} & & \\ & V = \left\{ \frac{-51}{20} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+42} & = & \color{red}{245x} +20 \\\Leftrightarrow & -210x \color{red}{+42} \color{blue}{-42} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{-42} \\\Leftrightarrow & -210x-245x& = & 20-42 \\\Leftrightarrow & \color{red}{-455} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-455} & & \\\Leftrightarrow & x = \frac{22}{455} & & \\ & V = \left\{ \frac{22}{455} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{-20} & = & \color{red}{21x} +4 \\\Leftrightarrow & 60x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & 60x-21x& = & 4+20 \\\Leftrightarrow & \color{red}{39} x& = & 24 \\\Leftrightarrow & x = \frac{24}{39} & & \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)